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(AUTOMATIC EDIT of page 2 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
 
(AUTOMATIC EDIT of page 2 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Confidence, ascending: False.)
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== List ==
 
== List ==
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1. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i1200404.png ; $f ( z ) = \frac { 1 } { ( 2 \pi i ) ^ { N } } \int _ { b _ { 0 } P } \frac { f ( \zeta ) d \zeta _ { 1 } \ldots d \zeta _ { N } } { ( \zeta _ { 1 } - z _ { 1 } ) \ldots ( \zeta _ { N } - z _ { N } ) } , z \in P$ ; confidence 0.186
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1. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620191.png ; $\sqrt { x }$ ; confidence 1.000
  
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2. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840308.png ; $U = \left( \begin{array} { l l } { U _ { 11 } } & { U _ { 12 } } \\ { U _ { 21 } } & { U _ { 22 } } \end{array} \right) : K \oplus \kappa _ { 1 } \rightarrow \sim \oplus \kappa _ { 2 }$ ; confidence 0.092
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2. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f130090107.png ; $( r - 1 )$ ; confidence 1.000
  
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3. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120130/k1201302.png ; $= \sum _ { \nu = 1 } ^ { n } \alpha _ { i \nu } f ( x _ { \nu } ) + \sum _ { \rho = 1 } ^ { i } \sum _ { \nu = 1 } ^ { 2 ^ { \rho - 1 } ( n + 1 ) } \beta _ { \imath \rho \nu } f ( \xi _ { \nu } ^ { \rho } )$ ; confidence 0.421
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3. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007034.png ; $196883 + 1$ ; confidence 1.000
  
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4. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120100/w12010032.png ; $\square ^ { \prime \prime } \Gamma _ { r k } ^ { t } = \{ \square _ { r k } ^ { t } \} - \frac { 1 } { 2 } g ^ { t s } ( \gamma _ { k } m _ { r s } + \gamma _ { r } m _ { s k } - \gamma _ { s } m _ { r k } )$ ; confidence 0.646
+
4. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g130050109.png ; $( d + 1 )$ ; confidence 1.000
  
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5. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011041.png ; $H ( u , v ) ( x , \xi ) = 2 ^ { n } \langle \sigma _ { x } , \xi u , v \rangle _ { L } ^ { 2 } ( R ^ { n } ) , ( \sigma _ { x } , \xi u ) ( y ) = u ( 2 x - y ) \operatorname { exp } ( - 4 i \pi ( x - y ) . \xi$ ; confidence 0.164
+
5. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026850/c0268508.png ; $f , g$ ; confidence 1.000
  
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6. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z1200107.png ; $[ e _ { i } , e _ { j } ] = ( \left( \begin{array} { c } { i + j + 1 } \\ { j } \end{array} \right) - \left( \begin{array} { c } { i + j + 1 } \\ { i } \end{array} \right) ) e _ { i + j }$ ; confidence 0.141
+
6. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170241.png ; $T ( 4 )$ ; confidence 1.000
  
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7. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007077.png ; $Q ( x ) \geq \operatorname { Clog } x \operatorname { log } \operatorname { log } x / ( \operatorname { log } \operatorname { log } \operatorname { log } x ) ^ { 2 }$ ; confidence 0.923
+
7. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c1300703.png ; $f ( X , Y ) = 0$ ; confidence 1.000
  
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8. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a1201104.png ; $\varphi ( \alpha , 0 , i ) = \alpha \text { for } i \geq 3 , \varphi ( \alpha , b , i ) = \varphi ( \alpha , \varphi ( \alpha , b - 1 , i ) , i - 1 ) \text { for } i \geq 1 , b \geq 1$ ; confidence 0.829
+
8. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120040/h12004033.png ; $G ( \omega , \omega )$ ; confidence 1.000
  
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9. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k } \\ { x _ { 1 } ( a b ) } & { \text { if } i \neq 1 , j = k } \end{array} \right.$ ; confidence 0.381
+
9. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180203.png ; $0 < p \leq 4$ ; confidence 1.000
  
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10. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011026.png ; $( \alpha ^ { w } ) ^ { * } = \operatorname { Op } ( J ( \overline { ( J ^ { 1 / 2 } \alpha ) } ) = \operatorname { Op } ( J ^ { 1 / 2 } \overline { a } ) = ( \overline { \alpha } ) ^ { w }$ ; confidence 0.090
+
10. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m13026035.png ; $( \lambda , \rho )$ ; confidence 1.000
  
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11. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007026.png ; $\leq K _ { 0 } \sum _ { i = 1 } ^ { k } ( t - s ) ^ { \alpha _ { i } } | \lambda | ^ { \beta _ { i } - 1 } , \lambda \in S _ { \theta _ { 0 } } \backslash \{ 0 \} , \quad 0 \leq s \leq t \leq T$ ; confidence 0.837
+
11. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030024.png ; $\gamma ( X ( t ) )$ ; confidence 1.000
  
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12. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020042.png ; $P ( t ) = \prod _ { m = 1 } ^ { n } ( t - t _ { m } ) ^ { \gamma _ { m } } ; \quad q _ { i } ( t ) = \{ \frac { ( t - t _ { i } ) ^ { \gamma _ { i } } } { P ( t ) } \} _ { \langle r _ { i } - 1 ; t _ { i } \rangle }$ ; confidence 0.111
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022084.png ; $p > 3$ ; confidence 1.000
  
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13. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003044.png ; $\rightarrow H ^ { \bullet } ( \Gamma \backslash X , \tilde { M } ) \stackrel { r } { \rightarrow } H ^ { \bullet } ( \partial ( \Gamma \backslash X ) , \tilde { M } )$ ; confidence 0.175
+
13. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006029.png ; $\int \rho = N$ ; confidence 1.000
  
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14. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230115.png ; $\omega \wedge L _ { K } = L ( \omega \wedge K ) + ( - 1 ) ^ { q + k - 1 } i ( d \omega \wedge K ) , [ \omega \wedge L _ { 1 } , L _ { 2 } ] ^ { \wedge } = \omega \wedge [ L _ { 1 } , L _ { 2 } ] +$ ; confidence 0.149
+
14. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e120260122.png ; $B ( n , p )$ ; confidence 1.000
  
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15. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055060/k0550606.png ; $\omega = i \partial \overline { \partial } p = i \sum \frac { \partial ^ { 2 } p } { \partial z _ { \alpha } \partial z _ { \beta } } d z _ { \alpha } \wedge d z _ { \beta }$ ; confidence 0.656
+
15. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021047.png ; $u ( z , \lambda )$ ; confidence 1.000
  
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16. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120070/l12007033.png ; $w = \frac { 1 } { s } \left( \begin{array} { c } { 1 } \\ { p _ { 1 } / r } \\ { p _ { 1 } p _ { 2 } / r ^ { 2 } } \\ { \vdots } \\ { p _ { 1 } \dots p _ { k } - 1 / r ^ { k - 1 } } \end{array} \right)$ ; confidence 0.466
+
16. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012330/a01233047.png ; $f ^ { - 1 } ( y )$ ; confidence 1.000
  
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17. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016039.png ; $X = ( X _ { 1 } , X _ { 2 } ) , M = ( M _ { 1 } , M _ { 2 } ) , \Phi = \left( \begin{array} { c c } { \Phi _ { 11 } } & { \Phi _ { 12 } } \\ { \Phi _ { 21 } } & { \Phi _ { 22 } } \end{array} \right)$ ; confidence 0.859
+
17. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023180/c02318027.png ; $2 n - 2$ ; confidence 1.000
  
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18. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001083.png ; $A ( \alpha ^ { \prime } , \alpha , k ) \approx - \frac { k ^ { 2 } V } { 4 \pi } ( 1 + \beta _ { p q } \alpha _ { q } \alpha _ { p } ^ { \prime } ) \text { if } \Gamma u = u _ { N } , k a \ll 1$ ; confidence 0.645
+
18. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z1200209.png ; $71 = 55 + 13 + 3$ ; confidence 1.000
  
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19. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060112.png ; $l _ { E } - i \Phi ( \xi _ { 1 } A _ { 1 } + \xi _ { 2 } A _ { 2 } - \xi _ { 1 } \lambda _ { 1 } - \xi _ { 2 } \lambda _ { 2 } ) ^ { - 1 } \Phi ^ { * } ( \xi _ { 1 } \sigma _ { 1 } + \xi _ { 2 } \sigma _ { 2 } )$ ; confidence 0.239
+
19. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a01297086.png ; $p ^ { \prime } = p / ( p - 1 )$ ; confidence 1.000
  
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20. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013036.png ; $\{ T _ { \lambda } : \lambda \in SP ^ { + } ( n ) \} \cup \{ T _ { \lambda } , T _ { \lambda } ^ { \prime } = \operatorname { sgn } . T _ { \lambda } : \lambda \in SP ^ { - } ( n ) \}$ ; confidence 0.955
+
20. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005037.png ; $\rho ( A ( t ) )$ ; confidence 1.000
  
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21. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070119.png ; $R = q ^ { - 1 / 2 } \left( \begin{array} { c c c c } { q } & { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { q - q ^ { - 1 } } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } & { q } \end{array} \right)$ ; confidence 0.879
+
21. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019045.png ; $\alpha = 1 / 2$ ; confidence 1.000
  
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22. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005092.png ; $\left\{ \begin{array} { l } { j _ { 1 } \geq \ldots \geq j _ { s } } \\ { i _ { s } \geq j _ { s } \geq 0 \quad \forall s , 1 \leq s \leq r } \\ { j _ { 1 } > 0 } \end{array} \right.$ ; confidence 0.351
+
22. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130160/f13016054.png ; $\mu ( M , P )$ ; confidence 1.000
  
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23. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070118.png ; $+ \frac { 1 } { 2 } ( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 4 \delta } } )$ ; confidence 0.399
+
23. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002035.png ; $( k - 1 ) ^ { 2 }$ ; confidence 1.000
  
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24. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120170/w12017017.png ; $\omega _ { \alpha + 1 } ( G ) / \omega _ { \alpha } ( G ) = \omega ( G / \omega _ { \alpha } ( G ) ) , \omega _ { \lambda } ( G ) = \cup _ { \beta < \lambda } \omega _ { \beta } ( G )$ ; confidence 0.993
+
24. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002048.png ; $21 + 8 + 2 = 31$ ; confidence 1.000
  
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25. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010064.png ; $\int _ { \Omega } u \Delta u d x = \int _ { \partial \Omega } u \frac { \partial u } { \partial \eta } d \sigma - \int _ { \Omega } | \operatorname { grad } u | ^ { 2 } d x$ ; confidence 0.983
+
25. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023052.png ; $0 = f ^ { \prime } ( 0 ) =$ ; confidence 1.000
  
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26. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b120270105.png ; $\operatorname { lim } _ { t \rightarrow \infty } \operatorname { Eh } ( Z ( t ) ) = \frac { \int _ { 0 } ^ { \infty } b ( u ) d u } { \int _ { 0 } ^ { \infty } P ( T _ { 1 } > u ) d u } =$ ; confidence 0.454
+
26. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007058.png ; $\theta ( 0 ) = 0$ ; confidence 1.000
  
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27. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030058.png ; $A ( \eta ) = - \sum _ { k , 1 = 1 } ^ { N } ( \frac { \partial } { \partial y _ { k } } + i \eta _ { k } ) ( \alpha _ { k l } ( y ) ( \frac { \partial } { \partial y _ { 1 } } + i \eta _ { l } ) )$ ; confidence 0.172
+
27. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l12009078.png ; $A \times \{ 0 \}$ ; confidence 1.000
  
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28. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001034.png ; $\frac { \partial v } { \partial t } = - \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } - 2 ( v \frac { \partial u } { \partial x } + u \frac { \partial v } { \partial x } )$ ; confidence 0.935
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28. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030710/d03071014.png ; $4 \pi$ ; confidence 1.000
  
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29. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002037.png ; $S _ { k } = E [ \left( \begin{array} { l } { X } \\ { k } \end{array} \right) ] = \sum _ { i = 1 } ^ { n } \left( \begin{array} { l } { i } \\ { k } \end{array} \right) p _ { i }$ ; confidence 0.071
+
29. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150103.png ; $B ( n , 1 / 2 )$ ; confidence 1.000
  
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30. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i12005053.png ; $\operatorname { lim } _ { n \rightarrow \infty } \alpha _ { n } = 0 = \operatorname { lim } _ { n \rightarrow \infty } n ^ { - 1 } \operatorname { log } \alpha _ { n }$ ; confidence 0.488
+
30. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110160/c11016038.png ; $[ 0,1 ]$ ; confidence 1.000
  
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31. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520263.png ; $\left\| \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right\| \mapsto \left\| \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right\|$ ; confidence 0.825
+
31. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007061.png ; $q ( 1 ) = 0$ ; confidence 1.000
  
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32. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041010.png ; $\| p \| _ { s } ^ { 2 } = \sum _ { i = 0 } ^ { N } \lambda _ { i } \int _ { R } | p ^ { ( i ) } ( t ) | ^ { 2 } d \mu _ { i } = \sum _ { i = 0 } ^ { N } \lambda _ { i } \| p ^ { ( i ) } ( t ) \| _ { \mu _ { i } } ^ { 2 }$ ; confidence 0.270
+
32. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005073.png ; $D ( A ( t ) )$ ; confidence 1.000
  
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33. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026011.png ; $\Gamma ( L ^ { 2 } ( R ) ) = \oplus _ { n = 0 } ^ { \infty } \sqrt { n ! L ^ { 2 } } ( R ) \overline { \otimes } ^ { n } \simeq \oplus _ { n = 0 } ^ { \infty } \sqrt { n ! L ^ { 2 } ( R ^ { n } ) }$ ; confidence 0.117
+
33. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120010/i12001018.png ; $\sigma ( 0 ) = 0$ ; confidence 1.000
  
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34. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065032.png ; $D _ { \mu } ( z ) = \operatorname { exp } \{ \frac { 1 } { 4 \pi } \int _ { - \pi } ^ { \pi } \operatorname { log } \mu ^ { \prime } ( \theta ) R ( e ^ { i \theta } , z ) d \theta \}$ ; confidence 0.988
+
34. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005039.png ; $i ( p - n + i )$ ; confidence 1.000
  
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35. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014048.png ; $[ X ] \mapsto \chi _ { Q } ( [ X ] ) = \operatorname { dim } _ { K } \operatorname { End } _ { Q } ( X ) - \operatorname { dim } _ { K } \operatorname { Ext } _ { Q } ^ { 1 } ( X , X )$ ; confidence 0.661
+
35. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130020/a13002015.png ; $\mu ( A ) = 0$ ; confidence 1.000
  
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36. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013022.png ; $\frac { \partial \Psi _ { i } } { \partial x _ { n } } = ( L ^ { n _ { 1 } } ) _ { + } \Psi _ { i } , \frac { \partial \Psi _ { i } } { \partial y _ { n } } = ( L _ { 2 } ^ { n } ) _ { - } \Psi _ { i }$ ; confidence 0.716
+
36. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130110/b13011026.png ; $\{ p ( t ) : 0 \leq t \leq 1 \}$ ; confidence 1.000
  
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37. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007055.png ; $\operatorname { ln } q ^ { \prime } = \frac { s } { \pi } P \int _ { 0 } ^ { 1 } \frac { \theta ^ { \prime } ( s ^ { \prime } ) d s ^ { \prime } } { s ^ { \prime } ( s ^ { \prime } - s ) }$ ; confidence 0.993
+
37. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130110/t13011034.png ; $( T , - )$ ; confidence 1.000
  
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38. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130040/z13004026.png ; $c = \operatorname { lim } _ { n \rightarrow \infty } \operatorname { cr } ( K _ { \alpha , n } ) \left( \begin{array} { l } { n } \\ { 2 } \end{array} \right) ^ { - 2 }$ ; confidence 0.265
+
38. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600224.png ; $( \alpha , \beta )$ ; confidence 1.000
  
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39. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230161.png ; $\left( \begin{array} { c } { 0 } \\ { G _ { i + 1 } } \end{array} \right) = \{ G _ { i } + Z _ { i } G _ { i } \frac { J g _ { i } ^ { * } g _ { i } } { g _ { j } J g _ { i } ^ { * } } \} \Theta _ { i }$ ; confidence 0.119
+
39. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015950/b0159504.png ; $B ( m , n )$ ; confidence 1.000
  
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40. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130040/k13004013.png ; $x _ { i } = \left\{ \begin{array} { l l } { 1 } & { \text { if } a _ { i } \leq c - \sum _ { j = 1 } ^ { i - 1 } a _ { j } x _ { j } } \\ { 0 } & { \text { otherwise } } \end{array} \right.$ ; confidence 0.821
+
40. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041060.png ; $\phi ( z ) = z + \sqrt { z ^ { 2 } - 1 }$ ; confidence 1.000
  
−
41. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006031.png ; $\left( \begin{array} { c } { \alpha _ { k - 1 } } \\ { k - 1 } \end{array} \right) \leq m - \left( \begin{array} { c } { \alpha _ { k } } \\ { k } \end{array} \right)$ ; confidence 0.229
+
41. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013610/a0136105.png ; $- \infty$ ; confidence 1.000
  
−
42. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l12016011.png ; $G _ { C } = \left\{ \begin{array}{l}{ \gamma \in L G _ { C } : \text { holomorphi } }\\{ \text { to a group' } ^ { \prime \prime } \square }\end{array} \right.$ ; confidence 0.174
+
42. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012460/a01246093.png ; $f ( t , x )$ ; confidence 1.000
  
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43. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130380/s13038052.png ; $K ( z , \delta ) : = \left\{ \begin{array}{l}{ t _ { i } = z _ { i } }\\{ ( t _ { 1 } , t _ { 2 } ) : | z _ { j } - t _ { j } | < \delta }\\{ i , j = 1,2 , i \neq j }\end{array} \right\}$ ; confidence 0.065
+
43. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008067.png ; $A ( t ) ^ { 1 / 2 }$ ; confidence 1.000
  
−
44. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s12022036.png ; $\sum _ { k = 0 } ^ { \infty } \operatorname { exp } ( - \lambda _ { j } t ) \sim ( 4 \pi t ) ^ { - \operatorname { dim } ( M ) / 2 } \sum _ { k = 0 } ^ { \infty } \alpha _ { k } t ^ { k }$ ; confidence 0.237
+
44. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027031.png ; $F ( 0 ) = 0$ ; confidence 1.000
  
−
45. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011060.png ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \stackrel { P } { \rightarrow } \alpha ( x ) = - \int _ { 0 } ^ { \infty } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } R ( d \lambda )$ ; confidence 0.493
+
45. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120240/b12024012.png ; $\{ \infty \}$ ; confidence 1.000
  
−
46. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008019.png ; $\left. \begin{array} { l } { \frac { d ^ { 2 } u } { d t ^ { 2 } } + A u = f ( t ) , \quad t \in [ 0 , T ] } \\ { u ( 0 ) = u _ { 0 } , \frac { d u } { d t } ( 0 ) = u _ { 1 } } \end{array} \right.$ ; confidence 0.668
+
46. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033210/d033210100.png ; $\lambda = ( \lambda _ { 1 } , \lambda _ { 2 } )$ ; confidence 1.000
  
−
47. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008035.png ; $\frac { f ^ { \prime } ( L ) } { f ( L ) } < \frac { g ^ { \prime } ( L ; m , s ) } { g ( L ; m , s ) } , \frac { f ^ { \prime } ( R ) } { f ( R ) } < \frac { g ^ { \prime } ( R ; m , s ) } { g ( R ; m , s ) }$ ; confidence 0.892
+
47. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001019.png ; $\operatorname { sgn } ( \sigma ) = 1$ ; confidence 1.000
  
−
48. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004027.png ; $f ( z ) = \operatorname { lim } _ { m \rightarrow \infty } \frac { 1 } { 2 \pi i } \int _ { \Gamma } f ( \zeta ) ( \frac { z } { \zeta } ) ^ { m } \frac { d \zeta } { \zeta - z }$ ; confidence 0.862
+
48. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002021.png ; $t \in ( 0,1 )$ ; confidence 1.000
  
−
49. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023058.png ; $G = \left( \begin{array} { c c c c c c c } { x _ { 0 } } & { \square \ldots } & { x _ { p - 1 } } & { y _ { 0 } } & { \square \ldots . \square } & { y _ { q - 1 } } \end{array} \right)$ ; confidence 0.056
+
49. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037010/e03701037.png ; $T ( A )$ ; confidence 1.000
  
−
50. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120090/e12009021.png ; $g _ { \mu \nu } = \left( \begin{array} { c c c c } { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } \end{array} \right)$ ; confidence 0.946
+
50. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030240/d0302404.png ; $| t | < \delta$ ; confidence 1.000
  
−
51. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024048.png ; $n _ { \Phi } L ( \varepsilon ) = 2 ( \operatorname { dim } _ { \Phi } U ( \varepsilon ) + \operatorname { dim } _ { \Phi } \{ K ( x , y ) \} _ { \operatorname { span } } )$ ; confidence 0.150
+
51. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007029.png ; $b = 5$ ; confidence 1.000
  
−
52. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005025.png ; $\hat { \psi } ( x , k ) \approx \left\{ \begin{array} { l l } { e ^ { - i k x } + b ( k ) } & { e ^ { i k x } } \\ { \alpha ( k ) e ^ { - i k x } } & { \text { as } x } \end{array} \right.$ ; confidence 0.203
+
52. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a013180166.png ; $( k - 1 )$ ; confidence 1.000
  
−
53. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004037.png ; $- \Delta t a \partial _ { \chi } ^ { ( 1 ) } u ( x _ { i } , t ^ { n } ) + \frac { \Delta t ^ { 2 } } { 2 } \alpha ^ { 2 } \partial _ { x } ^ { ( 2 ) } u ( x _ { i } , t ^ { n } ) + O ( \Delta t ^ { 2 } )$ ; confidence 0.085
+
53. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007017.png ; $p ^ { 2 } = m ^ { 2 }$ ; confidence 1.000
  
−
54. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015013.png ; $\left( \begin{array} { c c c } { x _ { 11 } } & { \dots } & { x _ { 1 x } } \\ { \vdots } & { \square } & { \vdots } \\ { x _ { p 1 } } & { \dots } & { x _ { p x } } \end{array} \right)$ ; confidence 0.515
+
54. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230150.png ; $A ^ { 2 } = A$ ; confidence 1.000
  
−
55. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003054.png ; $L u = \frac { \partial ^ { 2 } } { \partial x ^ { 2 } } ( E I ( x ) \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } ) + \rho A ( x ) \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } }$ ; confidence 0.965
+
55. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020066.png ; $\operatorname { sgn } ( \pi )$ ; confidence 1.000
  
−
56. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070117.png ; $\epsilon \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) = \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right)$ ; confidence 0.697
+
56. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016050.png ; $s ( n ) \geq \operatorname { log } n$ ; confidence 1.000
  
−
57. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050101.png ; $\sigma _ { p } = \sigma _ { 1 } = \sigma _ { \pi } = \sigma _ { \delta } = \sigma _ { r } = \sigma _ { T } = \sigma ^ { \prime } = \sigma ^ { \prime \prime } = \hat { \sigma }$ ; confidence 0.888
+
57. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070116.png ; $J ( z ) =$ ; confidence 1.000
  
−
58. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005046.png ; $K ( A , X ) : 0 \rightarrow \Lambda ^ { 0 } ( X ) \stackrel { D _ { A } ^ { 0 } } { 4 } \ldots \stackrel { D _ { A } ^ { n - 1 } } { \rightarrow } \Lambda ^ { n } ( X ) \rightarrow 0$ ; confidence 0.231
+
58. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021063.png ; $( 1,1,1,1 , R ) = ( 1,4 , R )$ ; confidence 1.000
  
−
59. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020189.png ; $\hat { t } \square ^ { * } : H ^ { n + 1 } ( \overline { D } \square ^ { n + 1 } , S ^ { n } ) \rightarrow H ^ { n + 1 } ( \Gamma _ { \square \square ^ { n + 1 } } , \Gamma _ { S ^ { n } } )$ ; confidence 0.204
+
59. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l0600408.png ; $f ( z ) = 0$ ; confidence 1.000
  
−
60. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010106.png ; $G _ { 2 } / \operatorname { Sp } ( 1 ) , \quad F _ { 4 } / \operatorname { Sp } ( 3 ) , E _ { 6 } / SU ( 6 ) , \quad E _ { 7 } / \operatorname { Spin } ( 12 ) , \quad E _ { 8 } / E _ { 7 }$ ; confidence 0.614
+
60. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130010/m13001043.png ; $R ( i )$ ; confidence 1.000
  
−
61. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005049.png ; $\leq B \sum _ { i = 1 } ^ { k } ( t - s ) ^ { \alpha _ { i } } | \lambda | ^ { \beta _ { i } - 1 } , \lambda \in S _ { \theta _ { 0 } } \backslash \{ 0 \} , \quad 0 \leq s \leq t \leq T$ ; confidence 0.804
+
61. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011033.png ; $\Gamma \subseteq B ( 0,1 )$ ; confidence 1.000
  
−
62. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004054.png ; $CF ( \zeta - z , w ) = \frac { ( n - 1 ) ! } { ( 2 \pi i ) ^ { n } } \frac { \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } w _ { k } d w [ k ] \wedge d \zeta } { \langle w , \zeta - z \rangle ^ { n } }$ ; confidence 0.204
+
62. https://www.encyclopediaofmath.org/legacyimages/r/r120/r120020/r12002010.png ; $g ( q )$ ; confidence 1.000
  
−
63. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120250/c1202505.png ; $= \int _ { \xi \in R ^ { 2 } } \left( \begin{array} { c c } { L _ { x } ^ { 2 } } & { L _ { x } L _ { y } } \\ { L _ { x } L _ { y } } & { L _ { y } ^ { 2 } } \end{array} \right) g ( x - \xi ; s ) d x$ ; confidence 0.382
+
63. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e1201202.png ; $f ( \theta , \phi )$ ; confidence 1.000
  
−
64. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008082.png ; $= \{ z \in \Delta : \operatorname { lim } _ { \omega \rightarrow \alpha } [ \rho ( z , \omega ) - \rho ( 0 , \omega ) ] < \frac { 1 } { 2 } \operatorname { log } R \}$ ; confidence 0.651
+
64. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004052.png ; $\lambda ^ { \prime } = ( 3,2,1,1 )$ ; confidence 1.000
  
−
65. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003081.png ; $\operatorname { Hom } _ { K _ { \infty } } ( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , C _ { \infty } ( \Gamma \backslash G ( R ) \otimes M _ { C } ) )$ ; confidence 0.214
+
65. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510106.png ; $\gamma ( F ( u ) ) = K$ ; confidence 1.000
  
−
66. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002074.png ; $+ \frac { n } { p _ { 1 } p _ { 2 } } + \ldots + \frac { n } { p _ { k - 1 } p _ { k } } + - \frac { n } { p _ { 1 } p _ { 2 } p _ { 3 } } - \ldots + ( - 1 ) ^ { k } \frac { n } { p _ { 1 } \ldots p _ { k } }$ ; confidence 0.552
+
66. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130140/r13014023.png ; $\sigma ( T ) = \{ 0 \}$ ; confidence 1.000
  
−
67. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i13003093.png ; $k _ { t } ( x , y ) = \operatorname { str } ( e ^ { - t D ^ { 2 } } ) = \operatorname { tr } ( e ^ { - t D _ { + } ^ { * } D _ { + } } ) - \operatorname { tr } ( e ^ { - t D _ { + } D _ { + } ^ { * } } )$ ; confidence 0.883
+
67. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005023.png ; $r ( 1,2 ) = 6$ ; confidence 1.000
  
−
68. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700052.png ; $( \lambda z ( x z ) ) [ x : = z z ] \equiv ( \lambda z ^ { \prime } \cdot ( x z ^ { \prime } ) ) [ x : = z z ] \equiv ( \lambda z ^ { \prime } ( ( z z ) z ^ { \prime } ) ) \not \equiv$ ; confidence 0.589
+
68. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013750/a0137508.png ; $A , B$ ; confidence 1.000
  
−
69. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015064.png ; $\times | I _ { p } + \Sigma ^ { - 1 } ( X - M ) \Omega ^ { - 1 } ( X - M ) ^ { \prime } | ^ { - ( n + m + p - 1 ) / 2 } , X \in R ^ { p \times n } , M \in R ^ { p \times n } , \Sigma > 0 , \Omega > 0$ ; confidence 0.800
+
69. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026013.png ; $D ( \mu )$ ; confidence 1.000
  
−
70. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027016.png ; $\frac { ( n - 1 ) ! } { ( 2 \pi i ) ^ { \frac { N } { N } } } \int _ { \partial D } \varphi \frac { \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } w _ { k } d w [ k ] \wedge d f } { \{ w , f \} ^ { N } } =$ ; confidence 0.149
+
70. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005056.png ; $2 d - 1$ ; confidence 1.000
  
−
71. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p130070103.png ; $\leq - \operatorname { log } ( \operatorname { max } \{ \operatorname { dist } ( z , \partial \Omega ) , \operatorname { dist } ( w , \partial \Omega ) \} )$ ; confidence 0.947
+
71. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050320/i05032047.png ; $f ( y ) = 0$ ; confidence 1.000
  
−
72. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011017.png ; $\partial _ { i } f _ { w } = \left\{ \begin{array} { l l } { 0 } & { ifl ( s _ { i } w ) > I ( w ) } \\ { f _ { s _ { i } w } } & { \text { ifl } ( s _ { i } w ) < 1 ( w ) } \end{array} \right.$ ; confidence 0.072
+
72. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l06003075.png ; $\sigma = \pi - A - B - C$ ; confidence 1.000
  
−
73. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010029.png ; $\operatorname { lim } _ { t \rightarrow \infty } \frac { f ( t ) ^ { 2 / d } } { t } \operatorname { log } P ( | W ^ { x } ( t ) | \leq f ( t ) ) = - \frac { 1 } { 2 } \lambda _ { d }$ ; confidence 0.556
+
73. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012039.png ; $[ - 1 / 2 , + \infty ]$ ; confidence 1.000
  
−
74. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007016.png ; $\frac { \partial } { \partial s } U ( t , s ) + U ( t , s ) A ( s ) = 0 , \operatorname { lim } _ { t \rightarrow s } U ( t , s ) x = x \text { for } x \in \overline { D ( A ( s ) ) }$ ; confidence 0.722
+
74. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007075.png ; $\eta \in ( 0,1 ]$ ; confidence 1.000
  
−
75. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130150/b1301504.png ; $\partial _ { t ^ { 2 } ( \Gamma , t ) } = ( 2 \pi i ) ^ { - 1 } PV \int _ { - \infty } ^ { \infty } \frac { d \Gamma ^ { \prime } } { z ( \Gamma , t ) - z ( \Gamma ^ { \prime } , t ) }$ ; confidence 0.346
+
75. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007071.png ; $\rho \in ( 0,1 ]$ ; confidence 1.000
  
−
76. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050026.png ; $l ( t , x ) = \operatorname { lim } _ { \epsilon \rightarrow 0 } \frac { 1 } { 2 \varepsilon } \int _ { 0 } ^ { t } 1 ( x - \varepsilon , x + \varepsilon ) ( W _ { s } ) d s$ ; confidence 0.183
+
76. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022084.png ; $F ( u ) = 0$ ; confidence 1.000
  
−
77. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004058.png ; $\phi _ { k } = \frac { 1 } { \{ \rho ^ { \prime } , \zeta \} ^ { N } } \{ \frac { \rho ^ { \prime } ( \zeta ) } { \{ \rho ^ { \prime } ( \zeta ) , \zeta \} } , z \} ^ { k } \sigma$ ; confidence 0.053
+
77. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006053.png ; $V ( f )$ ; confidence 1.000
  
−
78. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060129.png ; $Bel _ { X } = \operatorname { Bel } ^ { | X - R _ { T } | X - T - R } \oplus \operatorname { Bel } ^ { | X - T _ { R | X - T - R } } \oplus \operatorname { Bel } ^ { | X - T - R _ { X } }$ ; confidence 0.101
+
78. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010175.png ; $A ( E ) \rightarrow A ( E )$ ; confidence 1.000
  
−
79. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e1300501.png ; $0 = L ( \alpha , \beta ) u = \{ \partial _ { x } \partial _ { y } - \frac { \alpha - \beta } { x - y } \partial _ { x } + \frac { \alpha ( \beta - 1 ) } { ( x - y ) ^ { 2 } } \} u = 0$ ; confidence 0.992
+
79. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f12008042.png ; $\varphi = ( \xi , \eta )$ ; confidence 1.000
  
−
80. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023077.png ; $D _ { i } = \frac { \partial } { \partial x _ { i } } + y ^ { b _ { i } } \frac { \partial } { \partial y ^ { b } } + y ^ { b _ { i j } } \frac { \partial } { \partial y ^ { b _ { j } } }$ ; confidence 0.607
+
80. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222052.png ; $( n , n , n ) ^ { 2 }$ ; confidence 1.000
  
−
81. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007036.png ; $\prod _ { l = 1 } ^ { n } A ^ { \text { injout } } ( f _ { l } ) \Omega = \operatorname { lim } _ { t \rightarrow \pm \infty } \prod _ { l = 1 } ^ { n } A ( f _ { l } ^ { t } ) \Omega$ ; confidence 0.778
+
81. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520280.png ; $- \infty < \xi < \infty$ ; confidence 1.000
  
−
82. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001028.png ; $\operatorname { Im } A ( \alpha , \alpha , k ) = \frac { k } { 4 \pi } \int _ { S ^ { 2 } } | f ( \alpha , \beta , k ) | ^ { 2 } d \beta : = \frac { k \sigma ( \alpha ) } { 4 \pi }$ ; confidence 0.863
+
82. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660151.png ; $E = 0$ ; confidence 1.000
  
−
83. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120060/o12006068.png ; $\{ \lambda > 0 : \sum _ { | \alpha | = k - 1 } \int _ { \partial \Omega \times \partial \Omega } \Phi ( \frac { \Delta y - x F ( x ) } { | y - x | } ) \eta ( x , y ) \leq 1 \}$ ; confidence 0.789
+
83. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b130120103.png ; $p \in [ 1,2 ]$ ; confidence 1.000
  
−
84. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110222.png ; $S _ { \rho , \delta } ^ { \mu } = S ( \langle \xi \rangle ^ { \mu } , \langle \xi \rangle ^ { 2 \delta } | d x | ^ { 2 } + \langle \xi \rangle ^ { - 2 \rho } | d \xi | ^ { 2 } )$ ; confidence 0.406
+
84. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z1301209.png ; $p ( \xi ) = \eta$ ; confidence 1.000
  
−
85. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015079.png ; $= \frac { 1 } { n ! } \sum _ { \pi \text { a permutation } } d ( x _ { \pi } \langle 1 \rangle , \ldots , x _ { \pi } ( n ) ) , ( x _ { 1 } , \ldots , x _ { n } ) \in \{ 0,1 \} ^ { n }$ ; confidence 0.248
+
85. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a01197078.png ; $2 \pi$ ; confidence 1.000
  
−
86. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006017.png ; $\sigma f - f _ { x } = \operatorname { lim } _ { \delta \rightarrow 0 } D ^ { \pm } f = \operatorname { lim } _ { \delta \rightarrow 0 } ( x - x q ) ^ { - 1 } D ^ { \pm } f$ ; confidence 0.718
+
86. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c02514022.png ; $[ 0 , t ]$ ; confidence 1.000
  
−
87. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130030/d13003027.png ; $f ( x ) = \frac { 1 } { C _ { \psi } } \int _ { 0 } ^ { \infty } \int _ { - \infty } ^ { \infty } W _ { \psi } [ f ] ( a , b ) \psi ( \frac { x - b } { a } ) d b \frac { d a } { a \sqrt { a } }$ ; confidence 0.467
+
87. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120200/b12020063.png ; $U ( m , n )$ ; confidence 1.000
  
−
88. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230170.png ; $\Omega ( d L \Delta ) = \sum _ { | \alpha | = 0 } ^ { k } \frac { \partial L } { \partial y _ { \alpha } ^ { \alpha } } \omega _ { \alpha } ^ { \alpha } \otimes \Delta$ ; confidence 0.763
+
88. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a120180103.png ; $F ^ { \prime } ( x ) \neq 1$ ; confidence 1.000
  
−
89. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110010/h11001029.png ; $\operatorname { lim } _ { K \rightarrow \infty } \operatorname { sup } _ { x \geq 1 } \frac { 1 } { x } \cdot \sum _ { n \leq x , } \sum _ { f ( n ) } \quad | f ( n ) | = 0$ ; confidence 0.080
+
89. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w0975906.png ; $H ^ { 1 } ( k , A )$ ; confidence 1.000
  
−
90. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010052.png ; $R _ { 1414 } = \alpha _ { 1 } , R _ { 2323 } = \alpha _ { 1 } , R _ { 3434 } = \alpha _ { 2 } , R _ { 1234 } = \alpha _ { 1 } , R _ { 1324 } = - \alpha _ { 1 } , R _ { 1423 } = \alpha _ { 2 }$ ; confidence 0.632
+
90. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034085.png ; $u ( D ^ { 2 } )$ ; confidence 1.000
  
−
91. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004076.png ; $u _ { i } ^ { n + 1 } = \frac { 1 } { 2 } ( u _ { i } ^ { n } + \hat { a } _ { i } ^ { + } ) + \frac { 1 } { 2 } \frac { \Delta t } { \Delta x } ( \hat { f } _ { i - 1 } ^ { + } - \hat { f } _ { i } ^ { + } )$ ; confidence 0.584
+
91. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400127.png ; $w ( p - \delta ) + \delta$ ; confidence 1.000
  
−
92. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003037.png ; $\operatorname { IF } ( x ; T , F _ { \theta } ) = \frac { \Psi ( x , \theta ) } { \int \frac { \partial } { \partial \theta } \Psi ( y , \theta ) d F _ { \theta } ( y ) }$ ; confidence 0.678
+
92. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120040/h12004032.png ; $\xi < \lambda$ ; confidence 1.000
  
−
93. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130200/m13020010.png ; $0 \rightarrow H ^ { 0 } ( M ) \rightarrow C ^ { \infty } ( M ) \stackrel { H } { 4 } x ( M , \omega ) \stackrel { \gamma } { \rightarrow } H ^ { 1 } ( M ) \rightarrow 0$ ; confidence 0.075
+
93. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070191.png ; $R ^ { \prime } ( P ) = R ( P )$ ; confidence 1.000
  
−
94. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014051.png ; $\operatorname { lim } _ { \rho \rightarrow 0 } [ f ( x _ { 0 } + \gamma \rho n _ { 0 } ) - f _ { \rho } ^ { C } ( x _ { 0 } + \gamma \rho n _ { 0 } ) ] = D ( x _ { 0 } ) \psi ( \gamma )$ ; confidence 0.935
+
94. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010023.png ; $( \varphi \rightarrow \psi )$ ; confidence 1.000
  
−
95. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008087.png ; $\lambda \int _ { 0 } ^ { \infty } \frac { \int _ { 0 } ^ { x } y [ 1 - B ( y ) ] d y } { [ 1 - \rho ( x ) ] ^ { 2 } } d B ( x ) + \int _ { 0 } ^ { \infty } \frac { 1 - B ( x ) } { 1 - \rho ( x ) } d x$ ; confidence 0.507
+
95. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007092.png ; $G ( z , w )$ ; confidence 1.000
  
−
96. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008051.png ; $E [ T _ { p } ] _ { p R } = \frac { 1 } { 2 ( 1 - \sigma _ { p - 1 } ) ( 1 - \sigma _ { p } ) } \sum _ { k = 1 } ^ { p } \lambda _ { k } b _ { k } ^ { ( 2 ) } + \frac { b _ { p } } { 1 - \sigma _ { p - 1 } }$ ; confidence 0.504
+
96. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005056.png ; $\alpha \in ( 0,1 ]$ ; confidence 1.000
  
−
97. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620157.png ; $y \sim a \operatorname { cos } \int _ { c } ^ { x } ( \lambda - V _ { 1 } ( t ) ) ^ { 1 / 2 } d t + b \operatorname { sin } \int ^ { x _ { c } } ( \lambda - V _ { 1 } ( t ) ) ^ { 1 / 2 } d t$ ; confidence 0.312
+
97. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180155.png ; $\phi ( G ; s )$ ; confidence 1.000
  
−
98. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020088.png ; $\operatorname { exp } ( - 2 \theta n - 0.7823 \operatorname { log } n ) \leq M _ { 2 } \leq \operatorname { exp } ( - 2 \theta n + 4.5 \operatorname { log } n )$ ; confidence 0.964
+
98. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040156.png ; $\Omega \times G ( n , m )$ ; confidence 1.000
  
−
99. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w130090111.png ; $H _ { n _ { 1 } } ( \int _ { 0 } ^ { 1 } e _ { 1 } ( t ) d B ( t ) ) H _ { n _ { 2 } } ( \int _ { 0 } ^ { 1 } \rho _ { 2 } ( t ) d B ( t ) ) \ldots , n _ { j } \geq 0 , n _ { 1 } + n _ { 2 } + \ldots = n , n \geq 0$ ; confidence 0.330
+
99. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029029.png ; $f ( q ) = 0$ ; confidence 1.000
  
−
100. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040123.png ; $\| x \| _ { X } = \operatorname { sup } \{ | \int _ { \Omega } x x ^ { \prime } d \mu | : x ^ { \prime } \in X ^ { \prime } , \| x ^ { \prime } \| _ { X ^ { \prime } } \leq 1 \}$ ; confidence 0.322
+
100. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012059.png ; $b > 0$ ; confidence 1.000
  
−
101. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001094.png ; $= 2 \operatorname { Re } ( \sum _ { j , k } \rho _ { j k } ( \alpha ) w _ { j } w _ { k } ) + 2 \sum _ { j , k } \rho _ { j \overline { k } } ( \alpha ) w _ { j } \overline { w } _ { k }$ ; confidence 0.409
+
101. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f12019078.png ; $\{ 1 \} < N < G$ ; confidence 1.000
  
−
102. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015014.png ; $\left\{ \begin{array} { l } { x \square ^ { i } = f ^ { i } ( x ^ { 1 } , \ldots , x ^ { n } , t ) , \quad i = 1 , \ldots , n } \\ { \overline { t } = t } \end{array} \right.$ ; confidence 0.294
+
102. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n120020114.png ; $2 d + 4$ ; confidence 1.000
  
−
103. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004023.png ; $\| \alpha \| _ { \alpha _ { p } } = \sum _ { n = 0 } ^ { \infty } 2 ^ { n / p ^ { \prime } } \{ \sum _ { k = 2 ^ { n } } ^ { 2 ^ { n + 1 } - 1 } | \Delta d _ { k } | ^ { p } \} ^ { 1 / p } < \infty$ ; confidence 0.241
+
103. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130090/p13009042.png ; $\eta \in \partial \Omega$ ; confidence 1.000
  
−
104. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007025.png ; $A ( \alpha ^ { \prime } , \alpha , k ) = - \frac { 1 } { 4 \pi } \int _ { R ^ { 3 } } e ^ { i k \langle \alpha - \alpha ^ { \prime } \rangle x } q ( x ) d x + O ( \frac { 1 } { k } )$ ; confidence 0.292
+
104. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c02514043.png ; $t \in [ 0,1 ]$ ; confidence 1.000
  
−
105. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005034.png ; $= ( \frac { 2 } { \pi } ) ^ { 5 / 2 } \int _ { 0 } ^ { \infty } \operatorname { cosh } ( \pi \tau ) \operatorname { Re } K _ { 1 / 2 } + i \tau ( x ) F ( \tau ) G ( \tau ) d \tau$ ; confidence 0.718
+
105. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003052.png ; $Q = [ 0,1 ] \times [ 0,1 ]$ ; confidence 1.000
  
−
106. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001044.png ; $\underset { = \rightarrow 0 } { \operatorname { nsup } } \frac { 1 } { \varepsilon } \text { meas } \{ x : \rho ( x , \partial B ) < \varepsilon \} < \infty$ ; confidence 0.063
+
106. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065530/m0655301.png ; $[ - \pi , \pi )$ ; confidence 1.000
  
−
107. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013053.png ; $Q _ { \lambda } = \frac { 1 } { n ! } \sum _ { \pi \in O ( n ) } 2 ^ { ( r ( \lambda ) + r ( \pi ) + \epsilon ( \lambda ) ) / 2 } k _ { \pi } \zeta _ { \lambda } ^ { \pi } p _ { \pi }$ ; confidence 0.728
+
107. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010580/a01058026.png ; $( k + 1 )$ ; confidence 1.000
  
−
108. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020025.png ; $\operatorname { sup } _ { z _ { 1 } , \ldots , z _ { n } \in U } \operatorname { min } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { \phi } ( k ) }$ ; confidence 0.500
+
108. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010460/a01046080.png ; $f ( x )$ ; confidence 1.000
  
−
109. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110167.png ; $\operatorname { sup } _ { x \in K \atop \xi \in R ^ { n } } | ( D _ { x } ^ { \alpha } D _ { \xi } ^ { \beta } r _ { m - 2 } ) ( x , \xi ) | ( 1 + | \xi | ) ^ { 2 - m + | \beta | } < \infty$ ; confidence 0.218
+
109. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130200/m1302003.png ; $\{ f , g \} = P ( d f , d g )$ ; confidence 1.000
  
−
110. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230107.png ; $D _ { i } = \frac { \partial } { \partial x _ { i } } + \sum _ { | \alpha | = 0 } ^ { 2 k } y _ { \alpha + e _ { i } } ^ { b } \frac { \partial } { \partial y _ { \alpha } ^ { b } }$ ; confidence 0.482
+
110. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f1201503.png ; $B ( X , Y )$ ; confidence 1.000
  
−
111. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i12002010.png ; $\times \int _ { 0 } ^ { \infty } \tau \operatorname { sinh } ( \pi \tau ) S _ { \mu , i \tau } ( x ) | \Gamma ( \frac { 1 - \mu + i \tau } { 2 } ) | ^ { 2 } g ( \tau ) d \tau$ ; confidence 0.899
+
111. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120100/m12010032.png ; $\sigma ( y )$ ; confidence 1.000
  
−
112. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007024.png ; $q \in Q _ { m } : = \left\{ \begin{array} { c } { q = \overline { q } } \\ { q : | q ( x ) | + | \nabla ^ { m } q | \leq c ( 1 + | x | ) ^ { - b } } \\ { b > 3 } \end{array} \right.$ ; confidence 0.281
+
112. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m120130127.png ; $\lambda - \delta \xi > 0$ ; confidence 1.000
  
−
113. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003029.png ; $\operatorname { IF } ( x ; T , G ) = \frac { \partial } { \partial \varepsilon } [ T ( ( 1 - \varepsilon ) G + \varepsilon \Delta _ { X } ) ] \varepsilon = 0 +$ ; confidence 0.462
+
113. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090820/s09082025.png ; $\sigma ( X , Y )$ ; confidence 1.000
  
−
114. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060181.png ; $= \langle ( \xi _ { 1 } \sigma _ { 1 } + \xi _ { 2 } \sigma _ { 2 } ) u , u \rangle _ { E } - \langle ( \xi _ { 1 } \sigma _ { 1 } + \xi _ { 2 } \sigma _ { 2 } ) v , v \rangle _ { E }$ ; confidence 0.377
+
114. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072510/p07251032.png ; $\mu \neq 0$ ; confidence 1.000
  
−
115. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232050.png ; $\operatorname { lim } _ { r \rightarrow 1 } \int _ { E } | f ( r e ^ { i \theta } ) | ^ { \delta } d \theta = \int _ { E } | f ( e ^ { i \theta } ) | ^ { \delta } d \theta$ ; confidence 0.964
+
115. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130140/c13014019.png ; $A , B \in W$ ; confidence 1.000
  
−
116. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020019.png ; $\operatorname { inf } _ { z _ { j } \in U } \operatorname { max } _ { k \in S } \frac { \operatorname { Re } \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } } { M _ { d } ( k ) }$ ; confidence 0.333
+
116. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j12002074.png ; $\{ T = \infty \}$ ; confidence 1.000
  
−
117. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004052.png ; $= \operatorname { lim } _ { m \rightarrow \infty } \int _ { \Gamma } f ( \zeta ) [ CF ( \zeta - z , w ) - \sum _ { k = 0 } ^ { m } \frac { ( k + n - 1 ) } { k ! } \phi _ { k } ]$ ; confidence 0.553
+
117. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130080/m13008017.png ; $p = ( 1,1,00 )$ ; confidence 1.000
  
−
118. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e0350008.png ; $N _ { \epsilon } ( C , X ) = \operatorname { inf } \{ n : \exists x _ { 1 } , \ldots , x _ { n } , x _ { i } \in X : C \subset \cup _ { i = 1 } ^ { n } B ( x _ { i } , \epsilon ) \}$ ; confidence 0.657
+
118. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030077.png ; $2 ^ { 9 }$ ; confidence 1.000
  
−
119. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015012.png ; $\left\{ \begin{array} { l } { x \square ^ { i } = f ^ { i } ( x ^ { 1 } , \ldots , x ^ { n } ) , \quad i = 1 , \ldots , n } \\ { \overline { t } = t } \end{array} \right.$ ; confidence 0.434
+
119. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021031.png ; $m = 35$ ; confidence 1.000
  
−
120. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023060.png ; $D = \frac { \partial } { \partial x } + y ^ { \prime } \frac { \partial } { \partial y } + y ^ { \prime \prime } \frac { \partial } { \partial y ^ { \prime } }$ ; confidence 0.926
+
120. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130210/b13021034.png ; $g + g ^ { T }$ ; confidence 1.000
  
−
121. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090165.png ; $\Gamma = \operatorname { Gal } ( k _ { \chi , \infty } / k _ { \chi } ) \cong \operatorname { Gal } ( k _ { \chi } ( \mu _ { p } \infty ) / k _ { \chi } ( \mu _ { p } ) )$ ; confidence 0.650
+
121. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010046.png ; $\alpha \in [ 0 , + \infty ]$ ; confidence 1.000
  
−
122. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006055.png ; $= \int _ { 0 } ^ { \infty } | ( V \phi | \lambda ) | ^ { 2 } ( \frac { 1 } { \zeta - \lambda - i \epsilon } - \frac { 1 } { \zeta - \lambda + i \epsilon } ) d \lambda =$ ; confidence 0.755
+
122. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006015.png ; $G ( z ) = ( z - H ) ^ { - 1 }$ ; confidence 1.000
  
−
123. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023057.png ; $f _ { t , s } ( x ) = \operatorname { sup } _ { z \in H } \operatorname { inf } _ { y \in H } ( f ( y ) + \frac { 1 } { 2 t } \| z - y \| ^ { 2 } - \frac { 1 } { 2 s } \| x - z \| ^ { 2 } )$ ; confidence 0.941
+
123. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520195.png ; $A ^ { T } = A$ ; confidence 1.000
  
−
124. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020035.png ; $\operatorname { inf } _ { z _ { 1 } , \ldots , z _ { n } \in U } \operatorname { max } _ { k \in S } \frac { \operatorname { Re } g _ { 1 } ( k ) } { M _ { d } ( \dot { k } ) }$ ; confidence 0.262
+
124. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024036.png ; $h ( t ) \geq 0$ ; confidence 1.000
  
−
125. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021020.png ; $W = \left( \begin{array} { c c c c } { A } & { B } & { C } & { D } \\ { - B } & { A } & { - D } & { C } \\ { - C } & { D } & { A } & { - B } \\ { - D } & { - C } & { B } & { A } \end{array} \right)$ ; confidence 0.972
+
125. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130070/t1300705.png ; $\rho ( \tau )$ ; confidence 1.000
  
−
126. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026011.png ; $\omega = \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } \| x \| ^ { - n } x _ { j } d x _ { 1 } \wedge \ldots \wedge d x _ { j - 1 } \wedge d x _ { j + 1 } \wedge \ldots \wedge d x _ { n }$ ; confidence 0.401
+
126. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120040/h12004013.png ; $G ( \kappa , \lambda )$ ; confidence 1.000
  
−
127. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028097.png ; $\left\{ \begin{array} { l } { \Delta v = 0 } \\ { v = \phi \quad \text { on } \partial D } \\ { | v | \leq \frac { c } { | z | ^ { 2 n - 2 } } } \end{array} \right.$ ; confidence 0.121
+
127. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g130050105.png ; $( d - 1 )$ ; confidence 1.000
  
−
128. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024050.png ; $= \operatorname { dim } _ { \Phi } T ( \varepsilon ) + \operatorname { dim } _ { \Phi } \operatorname { Inn } \operatorname { Der } T ( \varepsilon )$ ; confidence 0.981
+
128. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007027.png ; $( p , q , t ) ( p ^ { \prime } , q ^ { \prime } , t ^ { \prime } ) =$ ; confidence 1.000
  
−
129. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120200/f12020012.png ; $\left( \begin{array} { c c c } { A _ { 1 } } & { \square } & { * } \\ { \square } & { \ddots } & { \square } \\ { 0 } & { \square } & { A _ { n } } \end{array} \right)$ ; confidence 0.977
+
129. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l0600303.png ; $B ^ { \prime } B$ ; confidence 1.000
  
−
130. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006070.png ; $\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$ ; confidence 0.363
+
130. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020103.png ; $\gamma \in ( 0 , \infty )$ ; confidence 1.000
  
−
131. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m0622206.png ; $\Omega ^ { \alpha } = \lambda _ { i } ^ { \alpha } \Omega ^ { i } , \quad \Delta \lambda _ { i } ^ { \alpha } \wedge \Omega ^ { i } = 0 , \quad i , j = 1 , \ldots , m$ ; confidence 0.437
+
131. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025038.png ; $\lambda \in [ 0,2 ]$ ; confidence 1.000
  
−
132. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520311.png ; $\times a ^ { * } ( x _ { 1 } ) \ldots a ^ { * } ( x _ { n } ) a ( y _ { 1 } ) \ldots a ( y _ { m } ) \prod _ { i = 1 } ^ { n } d \sigma ( x _ { i } ) \prod _ { j = 1 } ^ { m } d \sigma ( y _ { j } )$ ; confidence 0.315
+
132. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e120140102.png ; $( 1 \rightarrow \varphi ) = \varphi$ ; confidence 1.000
  
−
133. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067040.png ; $\dot { y } _ { 0 } ^ { k } ( \phi ) \dot { y } ^ { k } ( u ) = j _ { x } ^ { k } ( \phi \circ u ) , \quad j _ { 0 } ^ { k } ( \phi ) \in GL ^ { k } ( n ) , \quad j _ { X } ^ { k } ( u ) \in M _ { k }$ ; confidence 0.124
+
133. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023089.png ; $\{ x , y \}$ ; confidence 1.000
  
−
134. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064046.png ; $\alpha ( e ^ { i \theta } ) = b ( e ^ { i \theta } ) \prod _ { r = 1 } ^ { R } \omega _ { \alpha _ { r } , \beta _ { r } } ( e ^ { i \langle \theta - \theta _ { r } \rangle } )$ ; confidence 0.338
+
134. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130130/w13013053.png ; $W = 2 \pi ^ { 2 }$ ; confidence 1.000
  
−
135. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020022.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } ( \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | \psi ( k , n ) } { M _ { d } ( k ) } ) ^ { 1 / k }$ ; confidence 0.225
+
135. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120050/d12005059.png ; $f ( E )$ ; confidence 1.000
  
−
136. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110175.png ; $a _ { m - 1 } = b _ { m - 1 } - \frac { 1 } { 2 \iota } \sum _ { 1 \leq j \leq n } \frac { \partial ^ { 2 } b _ { m } } { \partial x _ { j } \partial \xi _ { j } } = h _ { m - 1 } ^ { s }$ ; confidence 0.096
+
136. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p1201207.png ; $g ^ { \prime }$ ; confidence 1.000
  
−
137. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009042.png ; $\| \theta _ { n } ( h _ { 1 } \otimes \ldots \otimes h _ { n } ) \| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } | h _ { 1 } \otimes \ldots \otimes h _ { n } | _ { H } \otimes _ { n }$ ; confidence 0.092
+
137. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018077.png ; $\xi ( t ) - \xi ( s )$ ; confidence 1.000
  
−
138. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c13004028.png ; $= \int _ { 1 } ^ { \infty } \frac { t \operatorname { log } ( t \pm t ^ { - 1 } ) } { 1 + t ^ { 4 } } d t = \frac { \pi } { 16 } \operatorname { log } 2 \pm \frac { G } { 4 }$ ; confidence 0.778
+
138. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001040.png ; $t = A ^ { - 4 }$ ; confidence 1.000
  
−
139. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008047.png ; $\sum _ { l = 0 } ^ { m } \left[ \begin{array} { l } { A _ { 1 } } \\ { A _ { 2 } } \end{array} \right] ( l _ { m } \otimes D _ { m - i } ) A _ { 1 } ^ { i } = 0 ( D _ { 0 } = I _ { n } )$ ; confidence 0.181
+
139. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p075660111.png ; $| \xi | \geq 1$ ; confidence 1.000
  
−
140. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120150/d12015030.png ; $= ( 4 q ^ { 2 t } \frac { q ^ { 2 t } - 1 } { q ^ { 2 } - 1 } , q ^ { 2 t - 1 } [ \frac { 2 ( q ^ { 2 t } - 1 ) } { q + 1 } + 1 ] , q ^ { 2 t - 1 } ( q - 1 ) \frac { q ^ { 2 t - 1 } + 1 } { q + 1 } , q ^ { 4 t - 2 } )$ ; confidence 0.945
+
140. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017033.png ; $= 0$ ; confidence 1.000
  
−
141. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028098.png ; $F ( f ) = F _ { \phi } ( f ) = \int _ { \partial D _ { m } } f ( z ) \sum ^ { n _ { k = 1 } } ( - 1 ) ^ { k - 1 } \frac { \partial _ { V } } { \partial z _ { k } } d z [ k ] \bigwedge d z$ ; confidence 0.085
+
141. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004027.png ; $U ( t ) = U _ { 0 } ( t )$ ; confidence 1.000
  
−
142. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007023.png ; $\sum _ { n \in l \atop ( n ( n ) , q ) = 1 } e ^ { 2 \pi i g ( n ) \overline { n } ( n ) / q } | \leq ( \operatorname { deg } ( g ) + \operatorname { deg } ( h ) ) \sqrt { q }$ ; confidence 0.058
+
142. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022800/c02280056.png ; $1$ ; confidence 1.000
  
−
143. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f120210108.png ; $+ z ^ { \lambda } \sum _ { j = 1 } ^ { \infty } z ^ { j } [ c _ { j } ( \lambda ) \pi ( \lambda + j ) + \sum _ { k = 0 } ^ { j - 1 } c _ { k } ( \lambda ) p _ { j - k } ( \lambda + k ) ]$ ; confidence 0.943
+
143. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030240/d03024010.png ; $\gamma ( 0 ) = 0$ ; confidence 1.000
  
−
144. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040142.png ; $P _ { L } ( e ^ { \pi i / 3 } , i ) = \varepsilon ( L ) i ^ { \operatorname { com } ( L ) - 1 } ( i \sqrt { 3 } ) ^ { \operatorname { dim } ( H _ { 1 } ( M ^ { ( 2 ) } , Z _ { 3 } ) ) }$ ; confidence 0.361
+
144. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m1201606.png ; $( p \times n )$ ; confidence 1.000
  
−
145. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008086.png ; $\langle \rho ^ { \prime } ( \xi ) , \xi - p \rangle ^ { \alpha } = \prod _ { j = 0 } ^ { m } \langle \rho ^ { \prime } ( \xi ) , \xi - p _ { j } \rangle ^ { \alpha } j$ ; confidence 0.811
+
145. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066069.png ; $T ( 1 )$ ; confidence 1.000
  
−
146. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055780/k05578011.png ; $F _ { i } ( \tau ) = \int _ { 0 } ^ { \infty } \frac { \sqrt { 2 \tau \operatorname { sinh } \pi \tau } } { \pi } \frac { K _ { i \tau } } { \sqrt { x } } f _ { i } ( x ) d x$ ; confidence 0.620
+
146. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007049.png ; $f ( x + h ) - f ( x )$ ; confidence 1.000
  
−
147. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070105.png ; $= \operatorname { lim } _ { x \rightarrow 0 } ( \sum _ { j n = 1 } ^ { J _ { n } } K ( x , y _ { j n } ) c _ { j n } , \sum _ { m n = 1 } ^ { J _ { n } } K ( x , y _ { m n } ) c _ { m n } ) _ { 1 } =$ ; confidence 0.120
+
147. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016031.png ; $( q \times n )$ ; confidence 1.000
  
−
148. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059053.png ; $\frac { d \psi ( t ) } { d t } = \frac { q ^ { 1 / 2 } } { 2 \kappa \sqrt { \pi } } e ^ { - \langle \operatorname { ln } t / 2 \kappa ) ^ { 2 } } , q = e ^ { - 2 \kappa ^ { 2 } }$ ; confidence 0.242
+
148. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120030/x1200309.png ; $( \theta , p )$ ; confidence 1.000
  
−
149. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035022.png ; $\hat { \theta } _ { N } = \operatorname { arg } \operatorname { min } _ { \theta \in D _ { M } } \sum _ { M } ^ { N _ { t } = 1 } 1 ( y ( t ) - f ( Z ^ { t - 1 } , t , \theta ) )$ ; confidence 0.304
+
149. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031650/d03165025.png ; $f _ { 1 } = f$ ; confidence 1.000
  
−
150. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007010.png ; $\Gamma _ { 0 } ( N ) = \{ \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) \in SL ( 2 , Z ) : c \equiv 0 ( \operatorname { mod } N ) \}$ ; confidence 0.549
+
150. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110630/b110630108.png ; $R G$ ; confidence 1.000
  
−
151. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w12005054.png ; $f _ { A } ( x + h ) = f ( x ) + \sum _ { | \alpha | \geq 1 } \frac { 1 } { \alpha ! } \frac { \partial ^ { | \alpha | } f } { \partial x ^ { \alpha } } | _ { x } h ^ { \alpha }$ ; confidence 0.741
+
151. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510131.png ; $\gamma ( w ) = \gamma ( u )$ ; confidence 1.000
  
−
152. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240278.png ; $P ( \hat { \psi } - S \hat { \sigma } _ { \hat { \psi } } \leq \psi \leq \hat { \psi } + S \hat { \sigma } _ { \hat { \psi } } , \forall \psi \in L ) = 1 - \alpha$ ; confidence 0.051
+
152. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f13029072.png ; $( Y , \sigma )$ ; confidence 1.000
  
−
153. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040227.png ; $\Gamma \approx \Delta \operatorname { mod } e l s _ { K } \varphi \approx \psi \text { iff } E ( \Gamma , \Delta ) \dagger _ { D } E ( \varphi , \psi )$ ; confidence 0.241
+
153. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011059.png ; $M = T ( h )$ ; confidence 1.000
  
−
154. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002023.png ; $= 2 ^ { 5 / 4 } 3 ^ { - 3 / 4 } ( t ( 1 - t ) ) ^ { 1 / 4 } \text { as., } n ^ { 1 / 4 } ( \alpha _ { n } ( t ) + \beta _ { n } ( t ) ) \stackrel { d } { \rightarrow } Z [ B ( t ) ] ^ { 1 / 2 }$ ; confidence 0.066
+
154. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012024.png ; $1$ ; confidence 1.000
  
−
155. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001041.png ; $\frac { \partial c } { \partial t } = \operatorname { div } \{ M \operatorname { grad } [ f _ { 0 } ^ { \prime } ( c ) - 2 \kappa \Delta c ] \} \text { in } V$ ; confidence 0.501
+
155. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015073.png ; $p \in [ 0,1 ]$ ; confidence 1.000
  
−
156. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028084.png ; $F ( f ) = F _ { \phi } ( f ) = \operatorname { lim } _ { \epsilon \rightarrow 0 } \int _ { \partial D _ { \epsilon } } f ( z ) \overline { \phi ( z ) } d \sigma$ ; confidence 0.895
+
156. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046320/h04632090.png ; $G ( z )$ ; confidence 1.000
  
−
157. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230104.png ; $E ^ { \vec { a } } ( L ) = \sum _ { | \alpha | = 0 } ^ { k } ( - 1 ) ^ { | \alpha | } D ^ { \alpha } ( \frac { \partial L } { \partial y _ { \alpha } ^ { \dot { \alpha } } } )$ ; confidence 0.077
+
157. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n066630125.png ; $\rho > 1 / 2$ ; confidence 1.000
  
−
158. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006047.png ; $\mu ( u , v , w ) = \# \{ ( \alpha ^ { \prime } , \beta ^ { \prime } ) \in A \times B : D \alpha ^ { \prime } \beta ^ { \prime } = D \xi \text { withw } = D \xi D \}$ ; confidence 0.290
+
158. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002076.png ; $\phi - f$ ; confidence 1.000
  
−
159. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130010/j13001043.png ; $\langle D | f \rangle = ( - 1 ) ^ { | f | } - _ { z } | f | - \operatorname { com } ( D _ { f , 1 } ) - \operatorname { com } ( D _ { f , 2 } ) + \operatorname { com } ( D )$ ; confidence 0.442
+
159. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014022.png ; $\rho ( f ) = 0$ ; confidence 1.000
  
−
160. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007069.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ^ { \prime } ( z ) = \angle F ^ { \prime } ( \omega ) = \omega \overline { \eta } d ( \omega )$ ; confidence 0.899
+
160. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017036.png ; $\beta _ { 0 } > 0$ ; confidence 1.000
  
−
161. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066960/n06696021.png ; $F _ { n } ( x ; \lambda ) = \sum _ { m = 0 } ^ { \infty } \sum _ { k = m + n / 2 } ^ { \infty } \frac { ( \lambda / 2 ) ^ { m } ( x / 2 ) ^ { k } } { m ! k ! } e ^ { - ( \lambda + x ) / 2 }$ ; confidence 0.801
+
161. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007056.png ; $x ^ { 3 } - x - 1$ ; confidence 1.000
  
−
162. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200139.png ; $\geq | z _ { k } + 1 | \geq \ldots \geq | z _ { k } | = 1 \geq \ldots \geq | z _ { k _ { 2 } } - 1 | > > \frac { m } { m + n } \geq | z _ { k _ { 2 } } | \geq \ldots \geq | z _ { x } |$ ; confidence 0.211
+
162. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120040/n1200409.png ; $G M$ ; confidence 1.000
  
−
163. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005069.png ; $= \sum _ { n \in Z } \sum _ { k \geq 0 } \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ( - 1 ) ^ { k } x _ { 1 } ^ { n - k } x _ { 2 } ^ { k } x _ { 0 } ^ { - n - 1 }$ ; confidence 0.448
+
163. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020064.png ; $| z _ { j } | = 1$ ; confidence 1.000
  
−
164. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009095.png ; $\mathfrak { S } _ { \{ 1 , \ldots , \lambda _ { 1 } \} } \times \mathfrak { S } _ { \{ \lambda _ { 1 } + 1 , \ldots , \lambda _ { 1 } + \lambda _ { 2 } \} } \times$ ; confidence 0.312
+
164. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008090.png ; $g = N - 1$ ; confidence 1.000
  
−
165. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013039.png ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right)$ ; confidence 0.875
+
165. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051047.png ; $G = ( V , U )$ ; confidence 1.000
  
−
166. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160110.png ; $y _ { i } = e ^ { i z } \prod _ { j = 1 } ^ { p _ { t } } x _ { i j } ^ { b j } \prod _ { j ^ { \prime } = p _ { t + 1 } } ^ { p } ( 1 + x _ { i j ^ { \prime } } ) ^ { b j ^ { \prime } } e ^ { \mu i }$ ; confidence 0.054
+
166. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007054.png ; $\theta ^ { \prime } = \theta - \pi$ ; confidence 1.000
  
−
167. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120120/b1201202.png ; $M = \operatorname { inf } _ { p \in N } \operatorname { sup } \{ r : \operatorname { exp } _ { p } \text { injective on } B _ { r } ( 0 ) \subset T _ { p } M \}$ ; confidence 0.410
+
167. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z13012032.png ; $\xi \in ( - 1,1 )$ ; confidence 1.000
  
−
168. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120280/b1202805.png ; $\prod _ { j = 1 } ^ { \infty } \frac { | \alpha | } { \alpha } \frac { z - \alpha } { 1 - \overline { \alpha } z } , \quad \sum ( 1 - | \alpha _ { j } | ) < \infty$ ; confidence 0.091
+
168. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001030.png ; $u ( \xi , \eta ) = 0$ ; confidence 1.000
  
−
169. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d1201403.png ; $D _ { n } ( x , \alpha ) = \sum _ { i = 0 } ^ { | n / 2 | } \frac { n } { n - i } \left( \begin{array} { c } { n - i } \\ { i } \end{array} \right) ( - a ) ^ { i } x ^ { n - 2 i }$ ; confidence 0.369
+
169. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022055.png ; $F ( q ) = 0$ ; confidence 1.000
  
−
170. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005020.png ; $= \frac { \Gamma ( \alpha + \beta ) } { \Gamma ( \alpha ) \Gamma ( \beta ) } \int _ { 0 } ^ { 1 } \tau ( x + ( y - x ) t ) t ^ { \beta - 1 } ( 1 - t ) ^ { \alpha - 1 } d t +$ ; confidence 0.946
+
170. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l06105016.png ; $f ( P ) > 0$ ; confidence 1.000
  
−
171. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006044.png ; $| \lambda - \alpha _ { i } , i | \cdot | x _ { i } | \leq \sum _ { j = 1 \atop j \neq i } ^ { n } | \alpha _ { i } , j | \cdot | x _ { j } | \leq r _ { i } ( A ) \cdot | x _ { i } |$ ; confidence 0.451
+
171. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006065.png ; $p ( \lambda _ { 1 } , \lambda _ { 2 } ) = 0$ ; confidence 1.000
  
−
172. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007095.png ; $\operatorname { sup } _ { \alpha ^ { \prime } \in S ^ { 2 } } | A _ { \delta } ( \alpha ^ { \prime } , \alpha ) - A ( \alpha ^ { \prime } , \alpha ) | < \delta$ ; confidence 0.975
+
172. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012018.png ; $f ( x ) > 0$ ; confidence 1.000
  
−
173. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001050.png ; $K _ { i } = \frac { 1 } { ( r - 1 ) ! } \operatorname { lim } _ { z \rightarrow z _ { i } } \frac { d ^ { n } } { d z ^ { - 1 } } [ ( z - z _ { i } ) ^ { r } \frac { h ( z ) } { g ( z ) } ]$ ; confidence 0.945
+
173. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p130070120.png ; $\delta ( z , w )$ ; confidence 1.000
  
−
174. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040309.png ; $\epsilon 0,0 ( x , y , z , w ) \approx \epsilon 0,1 ( x , y , z , w ) , \ldots , \epsilon _ { m - 1,0 } ( x , y , z , w ) \approx \epsilon _ { m - 1 } , 1 ( x , y , z , w )$ ; confidence 0.055
+
174. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009056.png ; $f ( z ) =$ ; confidence 1.000
  
−
175. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007074.png ; $\frac { n ^ { \prime } } { n } < 1 + C \frac { ( \operatorname { log } \operatorname { log } n ) ^ { 2 } } { \operatorname { log } n } , C = \text { const } > 0$ ; confidence 0.614
+
175. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005097.png ; $( d - 2 )$ ; confidence 1.000
  
−
176. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026045.png ; $\operatorname { deg } _ { B } [ f , \Omega , y ] = \operatorname { deg } _ { B } [ f , \Omega _ { 1 } , y ] + \operatorname { deg } _ { B } [ f , \Omega _ { 2 } , y ]$ ; confidence 0.654
+
176. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001041.png ; $T ( E )$ ; confidence 1.000
  
−
177. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029072.png ; $H _ { m } ^ { i } ( M ) = \operatorname { lim } _ { n \rightarrow \infty } \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } ^ { n } , M ) \quad ( i \in Z )$ ; confidence 0.734
+
177. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018023.png ; $\frac { 1 } { 2 \pi } d \theta$ ; confidence 1.000
  
−
178. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010168.png ; $f ( z ) = \sum _ { k = 1 } ^ { \infty } \frac { c _ { k } } { ( 1 + \langle z , \alpha _ { k 1 } \rangle \rangle \ldots ( 1 + \langle z , \alpha _ { k n } \rangle ) }$ ; confidence 0.178
+
178. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006074.png ; $A = A ( x , y )$ ; confidence 1.000
  
−
179. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300902.png ; $\left. \begin{array} { l } { U _ { 0 } ( x ) = 0 } \\ { U _ { 1 } ( x ) = 1 } \\ { U _ { n } ( x ) = x U _ { n - 1 } ( x ) + U _ { n - 2 } ( x ) , \quad n = 2,3 } \end{array} \right.$ ; confidence 0.497
+
179. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004020.png ; $\varphi \in \Gamma$ ; confidence 1.000
  
−
180. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006046.png ; $= \cup _ { \beta ^ { \prime } } D \alpha D \beta ^ { \prime } = \cup _ { \alpha ^ { \prime } , \beta ^ { \prime } } D \alpha ^ { \prime } \beta ^ { \prime }$ ; confidence 0.979
+
180. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110160/a11016010.png ; $O ( n ^ { 3 } )$ ; confidence 1.000
  
−
181. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004097.png ; $f = \int _ { \partial D } f \wedge K _ { Y } - \overline { \partial _ { z } } \int f \wedge K _ { Y - 1 } + \int _ { D } \overline { \partial } f \wedge K _ { Y }$ ; confidence 0.514
+
181. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005015.png ; $( n - i + 1 ) \times ( n - i + 1 )$ ; confidence 1.000
  
−
182. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009090.png ; $\varphi : X \rightarrow \Lambda ^ { r } \oplus _ { l = 1 } ^ { s } \Lambda / ( f _ { l } ( T ) ^ { l } ) \oplus \oplus _ { j = 1 } ^ { t } \Lambda / ( \pi ^ { m _ { j } } )$ ; confidence 0.103
+
182. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110271.png ; $| \xi | > 1$ ; confidence 1.000
  
−
183. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o1300108.png ; $u = e ^ { i k \alpha x } + v , \operatorname { lim } _ { r \rightarrow \infty } \int _ { | s | = r } | \frac { \partial v } { \partial | x | } - i k v | ^ { 2 } d s = 0$ ; confidence 0.441
+
183. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022013.png ; $\rho = \rho ( T ) = \operatorname { diam } ( T )$ ; confidence 1.000
  
−
184. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035034.png ; $\left\{ \begin{array} { r l r l } { X _ { N } = H ( N , X _ { N - 1 } , y ( N ) , u ( N ) ) } & { } & { } \\ { \theta } & { \theta } & { N = h ( X _ { N } ) } \end{array} \right.$ ; confidence 0.065
+
184. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130280/b13028047.png ; $[ T ( n ) , X ]$ ; confidence 1.000
  
−
185. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013045.png ; $= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$ ; confidence 0.240
+
185. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230149.png ; $( n - k ) / 2$ ; confidence 1.000
  
−
186. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008075.png ; $c _ { n } = \frac { 1 } { \sqrt { n } B ( \frac { n } { 2 } , \frac { 1 } { 2 } ) } = \frac { \Gamma ( \frac { n + 1 } { 2 } ) } { \sqrt { n \pi } \Gamma ( \frac { n } { 2 } ) }$ ; confidence 0.979
+
186. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012038.png ; $( 6 \times 6 )$ ; confidence 1.000
  
−
187. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180168.png ; $RCA _ { \omega } = SP \{ \langle \mathfrak { P } ( \square ^ { \omega } U ) , c _ { i } , Id _ { i j } \rangle _ { i , j \in \omega } : U _ { is } \text { aset } \}$ ; confidence 0.085
+
187. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583062.png ; $\{ T ( s ) \}$ ; confidence 1.000
  
−
188. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010017.png ; $\Phi ( q ) = \left\{ \begin{array} { l l } { + \infty } & { \text { if } | q | \leq \sigma } \\ { 0 } & { \text { if } | q | > \sigma } \end{array} \right.$ ; confidence 0.837
+
188. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120010/m12001029.png ; $p \in ( 0 , \infty )$ ; confidence 1.000
  
−
189. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030095.png ; $\omega \{ K _ { i } \} ( S _ { 1 } \ldots S _ { i } S _ { j S } ^ { * } \ldots S _ { j 1 } ^ { * } ) = \prod _ { k = 1 } ^ { r } \{ S _ { j _ { k } } , K _ { k } S _ { k } \} \delta _ { r , s }$ ; confidence 0.054
+
189. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015047.png ; $i ( A ^ { \prime } ) = - i ( A )$ ; confidence 1.000
  
−
190. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090170.png ; $\omega : \operatorname { Gal } ( k ( \mu _ { p } ) / k ) \rightarrow Z _ { p } ^ { \times } ( \omega ( \alpha ) \equiv \alpha \operatorname { mod } p )$ ; confidence 0.609
+
190. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080199.png ; $A ( K ) = A ( G )$ ; confidence 1.000
  
−
191. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m13014089.png ; $D _ { j , k } ( \alpha ) = \{ z : b _ { j } ^ { 1 } | z _ { 1 } - \alpha _ { 1 } | ^ { 2 } + \ldots + b _ { j } ^ { n } | z _ { \lambda } - a _ { \lambda } | ^ { 2 } < r _ { j , k } ^ { 2 } \}$ ; confidence 0.279
+
191. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540102.png ; $( \infty \times \infty )$ ; confidence 1.000
  
−
192. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m11011045.png ; $J _ { b - a } ( \sqrt { x } ) Y _ { b - a } ( \sqrt { x } ) = - \sqrt { x } x ^ { - a } G _ { 13 } ^ { 20 } ( x | \begin{array} { c } { a + 1 / 2 } \\ { b , a , 2 a - b } \end{array} )$ ; confidence 0.168
+
192. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009072.png ; $0 \leq i \leq n - 1$ ; confidence 1.000
  
−
193. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023044.png ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } } | \Sigma | ^ { - n / 2 } \operatorname { etr } \{ - \frac { 1 } { 2 } \Sigma ^ { - 1 } X X ^ { \prime } \} , X \in R ^ { p \times n }$ ; confidence 0.627
+
193. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040162.png ; $1 < p < 2$ ; confidence 1.000
  
−
194. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059050.png ; $\operatorname { lim } _ { n \rightarrow \infty } [ ( - z ) \frac { P _ { n } ( - z ) } { Q _ { n } ( - z ) } ] = z \int _ { 0 } ^ { \infty } \frac { d \psi ( t ) } { z + t }$ ; confidence 0.940
+
194. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120200/e12020022.png ; $( 1 + \epsilon )$ ; confidence 1.000
  
−
195. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130070/t13007035.png ; $\theta ( t ) - t = \frac { 1 } { 2 \pi } P.V. \int _ { 0 } ^ { 2 \pi } \operatorname { log } \rho ( \theta ( s ) ) \operatorname { cot } \frac { t - s } { 2 } d s$ ; confidence 0.583
+
195. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006034.png ; $\Gamma ( y )$ ; confidence 1.000
  
−
196. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120190/t12019013.png ; $t ( k , r ) = \operatorname { lim } _ { n \rightarrow \infty } \frac { T ( n , k , r ) } { \left( \begin{array} { l } { n } \\ { r } \end{array} \right) }$ ; confidence 0.746
+
196. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l1300605.png ; $[ 0,1 )$ ; confidence 1.000
  
−
197. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020091.png ; $M _ { 3 } = \operatorname { min } _ { z _ { j } } \operatorname { max } _ { k = 3 , \ldots , n + 2 } | s _ { k } | < \frac { 1 } { 1.473 ^ { n } } \text { for } n > n _ { 0 }$ ; confidence 0.317
+
197. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010520/a01052024.png ; $f ( n )$ ; confidence 1.000
  
−
198. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080123.png ; $\hat { \alpha } _ { i } = \alpha _ { i } ( u _ { k } , T _ { 1 } , T _ { n > 1 } = 0 ) = T _ { 1 } a _ { i } ( u _ { k } , \Lambda = 1 ) = a _ { i } ( \hat { u } _ { k } , \Lambda = T _ { 1 } )$ ; confidence 0.134
+
198. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110390/b11039063.png ; $A ( x , y )$ ; confidence 1.000
  
−
199. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040641.png ; $\langle M e _ { S } _ { P } \mathfrak { M } / \Omega F _ { S } \mathfrak { M } , F _ { S _ { P } } \mathfrak { M } / \Omega F _ { S } _ { P } \mathfrak { M } \rangle$ ; confidence 0.201
+
199. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016053.png ; $T = T _ { 1 } + K$ ; confidence 1.000
  
−
200. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036036.png ; $w ( a , b , c , d ) = w ( \square _ { \alpha } ^ { d } \square \square _ { b } ^ { c } ) = \operatorname { exp } ( - \frac { \epsilon ( a , b , c , d ) } { k _ { B } T } )$ ; confidence 0.134
+
200. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046320/h04632097.png ; $f ( z ) \in H ^ { 1 }$ ; confidence 1.000
  
−
201. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030270/d03027033.png ; $K _ { R , p } ( t ) = \frac { \operatorname { sin } ( ( 2 n + 1 - p ) t / 2 ) \operatorname { sin } ( ( p + 1 ) t / 2 ) } { 2 ( p + 1 ) \operatorname { sin } ^ { 2 } t / 2 }$ ; confidence 0.412
+
201. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021019.png ; $z = u ^ { \lambda }$ ; confidence 1.000
  
−
202. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021065.png ; $( \frac { \partial } { \partial \lambda } ) ^ { ( n _ { i } - 1 ) } u ( z , \lambda _ { i } ) = ( \operatorname { log } z ) ^ { n _ { i } - 1 } z ^ { \lambda _ { i } } +$ ; confidence 0.699
+
202. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080113.png ; $B ( X , X )$ ; confidence 1.000
  
−
203. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004051.png ; $\times \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } s _ { j } d s _ { 1 } \wedge \ldots \wedge [ d s _ { j } ] \wedge \ldots \wedge d s _ { n } \wedge \omega ( \zeta )$ ; confidence 0.178
+
203. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070130.png ; $f ( X , Y )$ ; confidence 1.000
  
−
204. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005016.png ; $\frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { \infty } \operatorname { cosh } ( \pi \tau ) | F ( \tau ) | ^ { 2 } d \tau = \int _ { 0 } ^ { \infty } | f ( x ) | ^ { 2 } d x$ ; confidence 0.997
+
204. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007041.png ; $n ( n - 2 ) - ( n - 1 ) ( n - 2 ) = n - 2$ ; confidence 1.000
  
−
205. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010145.png ; $\rho \leq \mathfrak { c } _ { 1 } ( \frac { \operatorname { ln } | \operatorname { ln } \delta | } { | \operatorname { ln } \delta | } ) ^ { c _ { 2 } }$ ; confidence 0.248
+
205. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010049.png ; $\lambda > 0$ ; confidence 1.000
  
−
206. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005076.png ; $\frac { I - \Theta _ { \Delta } ( z ) \Theta _ { \Delta } ( w ) ^ { * } } { 1 - z \overline { w } } = G ( I - z T ) ^ { - 1 } ( I - \overline { w } T ^ { * } ) ^ { - 1 } G ^ { * }$ ; confidence 0.941
+
206. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014059.png ; $( n , 6 ) = 1$ ; confidence 1.000
  
−
207. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004026.png ; $\lambda _ { 1 } ( \Omega ) = \operatorname { inf } _ { u \in H _ { 0 } ^ { 1 } ( \Omega ) } \frac { \int ( \nabla u ) ^ { 2 } d x } { \int _ { \Omega } u ^ { 2 } d x }$ ; confidence 0.462
+
207. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020076.png ; $[ \sqrt { n } , \sqrt { n + 1 } ]$ ; confidence 1.000
  
−
208. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008045.png ; $| f ( z _ { 0 } ) | ^ { 2 } \leq \frac { 1 } { \pi r ^ { 2 } } \int _ { D _ { z _ { 0 } , r } } | f ( \zeta ) | ^ { 2 } d x d y \leq \frac { 1 } { \pi r ^ { 2 } } ( f , f ) _ { L } 2 _ { ( D ) }$ ; confidence 0.280
+
208. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001053.png ; $x ( 1 ) = 0$ ; confidence 1.000
  
−
209. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025053.png ; $= 2 ( \frac { 2 n \operatorname { sin } \theta } { \pi } ) ^ { 1 / 2 } \operatorname { cos } \{ ( n + \frac { 1 } { 2 } ) \theta + \frac { \pi } { 4 } \} + O ( 1 )$ ; confidence 0.986
+
209. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m120030108.png ; $\int \rho ( u ) d \Phi ( u )$ ; confidence 1.000
  
−
210. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070146.png ; $p ^ { - 1 } \prod _ { m > 0 } ( 1 - p ^ { m } q ^ { n } ) ^ { c m n } = j ( w ) - j ( z ) , p = \operatorname { exp } ( 2 \pi i w ) , \quad q = \operatorname { exp } ( 2 \pi i z )$ ; confidence 0.474
+
210. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001086.png ; $( 3 m - 2 )$ ; confidence 1.000
  
−
211. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014049.png ; $\sigma ( T _ { \phi } ) = \sigma _ { e } ( T _ { \phi } ) \cup \{ \lambda \notin \sigma _ { e } ( T _ { \phi } ) : \text { ind } T _ { \phi - \lambda } \neq 0 \}$ ; confidence 0.895
+
211. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007011.png ; $\pm g$ ; confidence 1.000
  
−
212. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z1200101.png ; $O _ { 1 } ( m ) = \{ x ^ { ( i ) } : x ^ { ( i ) } x ^ { ( j ) } = \left( \begin{array} { c } { i + j } \\ { i } \end{array} \right) x ^ { ( i + j ) } , 0 \leq i , j < p ^ { m } \}$ ; confidence 0.461
+
212. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001054.png ; $x ( 2 ) = 1$ ; confidence 1.000
  
−
213. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013034.png ; $\phi _ { - } ^ { - 1 } \frac { \partial } { \partial t _ { \mu } } - Q _ { 0 } z ^ { \mu } \phi _ { - } = \frac { \partial } { \partial t _ { \mu } } - Q ^ { ( n ) }$ ; confidence 0.140
+
213. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130170/a13017034.png ; $( n - 1 )$ ; confidence 1.000
  
−
214. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031011.png ; $M _ { R } ^ { \delta } ( f ) ( x ) = \int _ { \{ \xi | \leq R } ( 1 - \frac { | \xi | ^ { 2 } } { R ^ { 2 } } ) ^ { \delta } e ^ { 2 \pi i x \cdot \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.073
+
214. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120030/x12003010.png ; $( - \theta , - p )$ ; confidence 1.000
  
−
215. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430126.png ; $\Delta u ^ { i } \square j = u ^ { i } \square _ { \alpha } \otimes u ^ { \alpha } \square j , \varepsilon u ^ { i } \square j = \delta ^ { i } \square$ ; confidence 0.336
+
215. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004090.png ; $( n , n - q - 1 )$ ; confidence 1.000
  
−
216. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008021.png ; $A = \left[ \begin{array} { l } { A _ { 1 } } \\ { A _ { 2 } } \end{array} \right] , \quad A _ { 1 } \in C ^ { n \times n } , A _ { 2 } \in C ^ { ( m - n ) \times n }$ ; confidence 0.847
+
216. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065027.png ; $\delta _ { \mu } > 0$ ; confidence 1.000
  
−
217. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030290/d03029016.png ; $E _ { n } ( f ) = \operatorname { inf } _ { \varepsilon _ { k } } \operatorname { sup } _ { x \in Q } | f ( x ) - \sum _ { k = 0 } ^ { n } c _ { k } s _ { k } ( x ) | \geq$ ; confidence 0.236
+
217. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b12006020.png ; $\epsilon = - 1$ ; confidence 1.000
  
−
218. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130010/g13001083.png ; $\operatorname { log } _ { \omega } ( \gamma \delta ) = \operatorname { log } _ { \omega } \gamma + \operatorname { log } _ { \omega } \delta$ ; confidence 0.964
+
218. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019011.png ; $f ( m )$ ; confidence 1.000
  
−
219. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130080/i13008014.png ; $X ^ { \prime } = L _ { 1 } ^ { \prime } \cap L _ { 2 } ^ { \prime } = L _ { 2 } ^ { \prime } \cap L _ { 3 } ^ { \prime } = L _ { 1 } ^ { \prime } \cap L _ { 3 } ^ { \prime }$ ; confidence 0.516
+
219. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a01160064.png ; $p > 2$ ; confidence 1.000
  
−
220. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004034.png ; $+ \Delta t \partial _ { t } ^ { ( 1 ) } u ( x _ { i } , t ^ { n } ) + \frac { \Delta t ^ { 2 } } { 2 } \partial _ { t } ^ { ( 2 ) } u ( x _ { i } , t ^ { n } ) + O ( \Delta t ^ { 2 } )$ ; confidence 0.911
+
220. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v09690078.png ; $\phi ( T ) < \infty$ ; confidence 1.000
  
−
221. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004074.png ; $u _ { + 1 / 2 } ^ { n + 1 / 2 } = \frac { 1 } { 2 } ( u _ { i } ^ { n } + u _ { i + 1 } ^ { n } ) + \frac { 1 } { 2 } \frac { \Delta t } { \Delta x } ( f _ { i } ^ { n } - f _ { i + 1 } ^ { n } )$ ; confidence 0.151
+
221. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015140/b01514018.png ; $f ^ { - 1 } ( 0 )$ ; confidence 1.000
  
−
222. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m120130130.png ; $N _ { 0 } = \frac { \lambda - \delta \xi } { 2 \alpha } , L _ { 0 } = \frac { 2 \beta N _ { 0 } + \gamma \xi ^ { p } - \varepsilon } { \mu _ { 1 } } , F _ { 0 } = \xi$ ; confidence 0.978
+
222. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035720/e03572015.png ; $f ( 0 ) \neq 0$ ; confidence 1.000
  
−
223. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006082.png ; $\mathfrak { V } ^ { ( l ) } = ( A _ { 1 } ^ { ( l ) } , A _ { 2 } ^ { ( l ) } , H ^ { ( l ) } , \Phi ^ { ( l ) } , E , \sigma _ { 1 } , \sigma _ { 2 } , \gamma , \tilde { \gamma } )$ ; confidence 0.768
+
223. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011490/a011490110.png ; $p > 0$ ; confidence 1.000
  
−
224. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r130080135.png ; $\sum _ { j = 1 } ^ { \infty } \lambda _ { j } ^ { - 1 } ( u , \varphi ; ) _ { 0 } \varphi _ { j } ( x ) = \sum _ { j = 1 } ^ { \infty } w _ { j } \varphi _ { j } ( x ) = w ( x )$ ; confidence 0.224
+
224. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007030.png ; $( \beta _ { k } | \beta _ { k } ) = 0$ ; confidence 1.000
  
−
225. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620133.png ; $\operatorname { lim } _ { N \rightarrow \infty } \frac { \int _ { 0 } ^ { N } | y ( x , \lambda ) | ^ { 2 } d x } { \int _ { | v ( x , \lambda ) | ^ { 2 } d x } } = 0$ ; confidence 0.169
+
225. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024057.png ; $( \varepsilon , \delta )$ ; confidence 1.000
  
−
226. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064052.png ; $\omega _ { \alpha , \beta } ( e ^ { i \theta } ) = ( 2 - 2 \operatorname { cos } \theta ) ^ { \alpha } e ^ { i \beta ( \theta - \pi ) } , 0 < \theta < 2 \pi$ ; confidence 0.592
+
226. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010039.png ; $\gamma \geq \Gamma$ ; confidence 1.000
  
−
227. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t120140134.png ; $\operatorname { dist } _ { \lambda } ( \phi , \psi ) = \operatorname { limsup } _ { S \rightarrow \lambda } | \phi ( \zeta ) - \psi ( \zeta ) |$ ; confidence 0.354
+
227. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011024.png ; $B ( 0 , r )$ ; confidence 1.000
  
−
228. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120030/w120030129.png ; $\Sigma ( \Gamma ) : = \{ f \in [ 0,1 ] ^ { \Gamma } : \begin{array} { c c } { f ( \gamma ) \neq 0 } \\ { \text { for at most countabl } } \end{array}$ ; confidence 0.135
+
228. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065016.png ; $H ( 0 ) = 1$ ; confidence 1.000
  
−
229. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019018.png ; $\psi _ { w } = \sum \lambda _ { i } \int _ { R ^ { 3 N } } e ^ { i p z / \hbar } \overline { \psi } _ { i } ( x + \frac { z } { 2 } ) \psi _ { i } ( x - \frac { z } { 2 } ) d z$ ; confidence 0.330
+
229. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120020/q12002040.png ; $\{ \lambda _ { 1 } , \lambda _ { 2 } \}$ ; confidence 1.000
  
−
230. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010075.png ; $y \forall v ( ( v \in x \bigwedge ( \neg v = \emptyset ) ) \rightarrow \exists s \forall t ( ( t \in v \wedge t \in y ) \leftrightarrow s = t ) )$ ; confidence 0.211
+
230. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007014.png ; $U ( t , s ) , 0 \leq s \leq t \leq T$ ; confidence 1.000
  
−
231. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210113.png ; $\operatorname { Ext } _ { a } ^ { i } ( M , N ) = \operatorname { Ker } \delta _ { i + 1 } ^ { \prime } / \operatorname { Im } \delta _ { i } ^ { \prime }$ ; confidence 0.700
+
231. https://www.encyclopediaofmath.org/legacyimages/w/w110/w110060/w11006020.png ; $C = C [ 0 , \infty )$ ; confidence 1.000
  
−
232. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027011.png ; $S _ { n } = \sum _ { 1 } ^ { n } X _ { i } \text { forn } \geq 1 , \text { and fort } \geq 0 , N ( t ) = k \text { if } S _ { k } \leq t < S _ { k + 1 } \text { for } k = 0,1$ ; confidence 0.586
+
232. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024014.png ; $N ( 0 , \sigma ^ { 2 } )$ ; confidence 1.000
  
−
233. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110220/d11022028.png ; $L y \equiv \rho _ { N } \frac { d } { d x } ( \rho _ { x } - 1 \cdots \frac { d } { d x } ( \rho _ { 1 } \frac { d } { d x } ( \rho _ { 0 } y ) ) \ldots ) , \rho _ { i } > 0$ ; confidence 0.155
+
233. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060128.png ; $f ( \lambda _ { 1 } , \lambda _ { 2 } ) = 0$ ; confidence 1.000
  
−
234. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120127.png ; $\Sigma ^ { ( t + 1 ) } = \frac { \sum _ { i } w _ { i } ^ { ( t + 1 ) } ( y _ { i } - \mu ^ { ( t + 1 ) } ) ( y _ { i } - \mu ^ { ( t + 1 ) } ) ^ { T } } { \sum _ { i } w _ { i } ^ { ( t + 1 ) } }$ ; confidence 0.890
+
234. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140120.png ; $( n ^ { 2 } \times n ^ { 2 } )$ ; confidence 1.000
  
−
235. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120100.png ; $\operatorname { log } \int f ( \theta , \phi ) d \phi = \operatorname { log } f ( \theta , \phi ) - \operatorname { log } f ( \phi | \theta ) =$ ; confidence 0.992
+
235. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h046010153.png ; $T ^ { 4 } \times [ 0,1 ]$ ; confidence 1.000
  
−
236. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049040.png ; $s _ { 1 } ^ { 2 } = \frac { 1 } { m - 1 } \sum _ { i } ( X _ { i } - X ) ^ { 2 } \quad \text { and } \quad s _ { 2 } ^ { 2 } = \frac { 1 } { n - 1 } \sum _ { j } ( Y _ { j } - Y ) ^ { 2 }$ ; confidence 0.954
+
236. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120120.png ; $f ( \theta , \phi , \alpha )$ ; confidence 1.000
  
−
237. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005043.png ; $\xi _ { j } = \varepsilon ( x _ { j } + \frac { 1 } { i } \frac { \partial \mu _ { 0 } } { \partial \dot { k } _ { i } } ( k _ { c } , R _ { c } ) t ) , j = 1 , \ldots , n$ ; confidence 0.427
+
237. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007088.png ; $\operatorname { log } \operatorname { log } n ) ^ { 3 }$ ; confidence 1.000
  
−
238. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002041.png ; $\Delta = \left( \begin{array} { l } { n } \\ { 4 } \end{array} \right) \left( \begin{array} { l } { 4 } \\ { 2 } \end{array} \right) p ^ { 5 }$ ; confidence 0.921
+
238. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001044.png ; $t \neq 0,1$ ; confidence 1.000
  
−
239. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j1200207.png ; $\| f \| _ { H ^ { p } } ^ { p } : = \frac { 1 } { 2 \pi } \operatorname { sup } _ { r < 1 } \int _ { - \pi } ^ { \pi } | f ( r e ^ { i \vartheta } ) | ^ { p } d \vartheta$ ; confidence 0.445
+
239. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m11011025.png ; $p + q < 2 ( m + n )$ ; confidence 1.000
  
−
240. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007012.png ; $m ( P ) = \operatorname { log } | a _ { 0 } | + \sum _ { k = 1 } ^ { d ^ { \prime } } \operatorname { log } ( \operatorname { max } ( | \alpha _ { k } | , 1 ) )$ ; confidence 0.311
+
240. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040140/f0401407.png ; $\alpha < \beta$ ; confidence 1.000
  
−
241. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130080/m13008035.png ; $A _ { f } ^ { t } = - 2 \int h _ { t } ( s ) \times [ \int _ { S ^ { 2 } } d \omega \times ( \frac { \partial } { \partial x ^ { 0 } } A ) _ { f } ( s , \omega s ) ] s d s$ ; confidence 0.966
+
241. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a1300803.png ; $f ( x ) \leq h ( x )$ ; confidence 1.000
  
−
242. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110116.png ; $\frac { D \phi } { D t } = \frac { \partial \phi } { \partial t } + v _ { i } \phi _ { , i } = \frac { \partial \phi } { \partial t } + ( v . \nabla ) \phi$ ; confidence 0.908
+
242. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007016.png ; $u = \pm x ^ { - 1 } g x$ ; confidence 1.000
  
−
243. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008067.png ; $\sum _ { i , j + 1 } ^ { n } K ( p _ { i } , p _ { j } ) \xi _ { j } \overline { \xi _ { i } } = \int _ { T } | \sum _ { j = 1 } ^ { n } \xi _ { j } h ( t , p _ { j } ) | ^ { 2 } d m ( t ) > 0$ ; confidence 0.662
+
243. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006018.png ; $b ( x )$ ; confidence 1.000
  
−
244. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140140.png ; $q ( x ) = \sum _ { i \in I } x _ { i } ^ { 2 } + \sum _ { i \prec j } x _ { i } x _ { j } - \sum _ { p \in \operatorname { max } l } ( \sum _ { i \prec p } x _ { i } ) x _ { p }$ ; confidence 0.197
+
244. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120080/l12008016.png ; $( 0 , y )$ ; confidence 1.000
  
−
245. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014056.png ; $A _ { Q } ( v ) = \prod _ { i , j \in Q _ { 0 } } \prod _ { \langle \beta : j \rightarrow i \rangle \in Q _ { 1 } } M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta }$ ; confidence 0.481
+
245. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003044.png ; $E ^ { \prime } = f ( E )$ ; confidence 1.000
  
−
246. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200108.png ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq c _ { m , n } , \operatorname { min } _ { j = 1 , \ldots , N } | b _ { 1 } + \ldots + b _ { j } |$ ; confidence 0.086
+
246. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007053.png ; $f ^ { \prime } ( N ) = B$ ; confidence 1.000
  
−
247. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200174.png ; $A = \frac { 1 } { 6 n } \operatorname { min } _ { n \leq x \leq 2 n } ( \frac { x } { 4 e ( m + x ) } ) ^ { x } | \operatorname { Re } \sum _ { j = 1 } ^ { n } b _ { j } |$ ; confidence 0.948
+
247. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130180/b13018018.png ; $0 < R < \infty$ ; confidence 1.000
  
−
248. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004027.png ; $g = - \frac { \omega _ { 1 } + i \omega _ { 2 } } { \omega _ { 3 } } = \frac { \omega _ { 3 } } { \omega _ { 1 } - i \omega _ { 2 } } , \eta = g ^ { - 1 } \omega _ { 3 }$ ; confidence 0.750
+
248. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013820/a0138205.png ; $g ( P )$ ; confidence 1.000
  
−
249. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130140/w13014013.png ; $g ( y ) = \left\{ \begin{array} { l l } { \frac { 1 } { \pi y } \operatorname { sin } 2 \pi y , } & { y \neq 0 } \\ { 2 , } & { y = 0 } \end{array} \right.$ ; confidence 0.715
+
249. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090163.png ; $\Delta ( \lambda ) ^ { \perp }$ ; confidence 1.000
  
−
250. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011057.png ; $\frac { \mu _ { n } ( x ) } { n } \stackrel { P } { \rightarrow } - \int _ { 0 } ^ { \infty } \frac { \lambda ^ { x } } { x ! } e ^ { - \lambda } G ( d \lambda )$ ; confidence 0.480
+
250. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s086520149.png ; $\phi ( T ) = 0$ ; confidence 1.000
  
−
251. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290169.png ; $h _ { \phi } = \operatorname { rank } _ { A } M - \sum _ { i = 1 } ^ { d - 1 } \left( \begin{array} { c } { d - 1 } \\ { i - 1 } \end{array} \right) h _ { i }$ ; confidence 0.379
+
251. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120070/h12007031.png ; $( n - k - 1 )$ ; confidence 1.000
  
−
252. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004048.png ; $\rho ^ { \prime } = \operatorname { grad } \rho = ( \partial \rho / \partial \zeta _ { 1 } , \dots , \partial \rho / \partial \zeta _ { n } )$ ; confidence 0.507
+
252. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032890/d03289086.png ; $0 < \sigma < 1$ ; confidence 1.000
  
−
253. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030270/d03027036.png ; $= \frac { 1 } { 2 } + \sum _ { k = 1 } ^ { n - p } \operatorname { cos } k t + \sum _ { k = 1 } ^ { p } ( 1 - \frac { k } { p + 1 } ) \operatorname { cos } ( n - p + k ) t$ ; confidence 0.991
+
253. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022075.png ; $i ^ { 2 } = - 1$ ; confidence 1.000
  
−
254. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006049.png ; $+ \frac { \{ U _ { i } = ( u _ { t } + 1 , \ldots , u _ { t } + k ) : s _ { j } < u + j \leq t _ { j } , 1 \leq j \leq k \} } { \# \{ U _ { i } = ( u _ { t } + 1 , \ldots , u + k ) \} }$ ; confidence 0.139
+
254. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130020/k13002044.png ; $\operatorname { sign } ( Y _ { 1 } - Y _ { 2 } )$ ; confidence 1.000
  
−
255. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060020/l06002013.png ; $\operatorname { lim } _ { l \rightarrow 0 } \Pi ( l ) = \frac { \pi } { 2 } , \quad \operatorname { lim } _ { l \rightarrow \infty } \Pi ( l ) = 0$ ; confidence 0.867
+
255. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110010/o1100106.png ; $P ( G ) \cup P ( G ) ^ { - 1 } = G$ ; confidence 1.000
  
−
256. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015063.png ; $\frac { \Gamma _ { p } [ \frac { ( n + m + p - 1 ) } { 2 } ] } { \pi ^ { m p / 2 } \Gamma _ { p } ( ( n + p - 1 ) / 2 ) } | \Sigma | ^ { - m / 2 } | \Omega | ^ { - p / 2 } \times$ ; confidence 0.513
+
256. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006040.png ; $f ^ { \prime } ( 0 ) \neq 0$ ; confidence 1.000
  
−
257. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m130230150.png ; $( ( X _ { n } + 1 , B _ { n + 1 } ) , f _ { n + 1 } ) = ( ( X _ { n } ^ { + } , ( \phi _ { * } ^ { + } ) ^ { - 1 } \phi _ { * } B _ { n } ) , f _ { n } \circ \phi ^ { - 1 } \circ \phi ^ { + } )$ ; confidence 0.337
+
257. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034034.png ; $D = U _ { 1 }$ ; confidence 1.000
  
−
258. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130040/n1300401.png ; $C _ { N } = \left( \begin{array} { c } { 2 n } \\ { n } \end{array} \right) - \left( \begin{array} { c } { 2 n } \\ { n - 1 } \end{array} \right)$ ; confidence 0.361
+
258. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a01300080.png ; $P ( z )$ ; confidence 1.000
  
−
259. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070134.png ; $\Delta t ^ { i } \square j = t ^ { i } \square _ { \alpha } \otimes t ^ { \alpha } \square j , \epsilon t ^ { i } \square j = \delta ^ { i } \square j$ ; confidence 0.251
+
259. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029014.png ; $f ( q ) = 1 / q ^ { 2 }$ ; confidence 1.000
  
−
260. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s1306409.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \operatorname { det } T _ { n } ( a ) } { \operatorname { det } T _ { n - 1 } ( a ) } = G ( a )$ ; confidence 0.569
+
260. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230105.png ; $( \omega \wedge D ) \varphi = \omega \wedge D ( \varphi )$ ; confidence 1.000
  
−
261. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011084.png ; $\frac { n } { \mu _ { n } } = \frac { \sum _ { x = 1 } ^ { n } x \mu _ { n } ( x ) } { \mu _ { n } } \sim \sum _ { x = 1 } ^ { n } \frac { 1 } { x + 1 } \rightarrow \infty$ ; confidence 0.294
+
261. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000
  
−
262. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d1200209.png ; $( L ) v ^ { * } = \left\{ \begin{array} { l l } { \operatorname { max } } & { g ( u _ { 1 } ) } \\ { s.t. } & { u _ { 1 } \in U _ { 1 } } \end{array} \right.$ ; confidence 0.276
+
262. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130050/n13005048.png ; $( s , r + 1 )$ ; confidence 1.000
  
−
263. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008090.png ; $= \{ z \in D : \operatorname { limsup } _ { w \rightarrow X } [ K _ { D } ( z , w ) - K _ { D } ( z _ { 0 } , w ) ] < \frac { 1 } { 2 } \operatorname { log } R \}$ ; confidence 0.675
+
263. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007017.png ; $\Gamma ( \omega , \alpha )$ ; confidence 1.000
  
−
264. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230172.png ; $l _ { i } = \delta _ { i } ^ { * } G _ { i } \Theta _ { i } \left( \begin{array} { c } { 1 } \\ { 0 } \end{array} \right) , d _ { i } = | \delta _ { i } | ^ { 2 }$ ; confidence 0.492
+
264. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120150/h12015035.png ; $G ( \phi )$ ; confidence 1.000
  
−
265. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015067.png ; $\frac { d ^ { 2 x ^ { i } } } { d t ^ { 2 } } + \gamma ^ { i j k } ( x ) \frac { d x ^ { j } } { d t } \frac { d x ^ { k } } { d t } = \lambda _ { ( i ) } \frac { d x ^ { i } } { d t }$ ; confidence 0.742
+
265. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412037.png ; $\sigma > 1$ ; confidence 1.000
  
−
266. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026034.png ; $P ( \theta , \mu ) ( d x ) = \sum _ { k = 0 } ^ { n } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) p ^ { k } q ^ { n - k } \delta _ { k } ( d x )$ ; confidence 0.477
+
266. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090149.png ; $\Delta ( \lambda )$ ; confidence 1.000
  
−
267. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010025.png ; $\{ \sum _ { n = 1 } ^ { \infty } N _ { p } ( k _ { n } ) N _ { p } , ( l _ { n } ) : \quad \text { with } u = \sum _ { n = 1 } ^ { \infty } \overline { k _ { n } } * r _ { n }$ ; confidence 0.134
+
267. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120090/m12009038.png ; $P ( \xi ) = 0$ ; confidence 1.000
  
−
268. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230114.png ; $= \omega \wedge [ D _ { 1 } , D _ { 2 } ] - ( - 1 ) ^ { ( q + k _ { 1 } ) k _ { 2 } } D _ { 2 } ( \omega ) \wedge D _ { 1 } , i ( \omega \wedge L ) = \omega \wedge i ( L )$ ; confidence 0.539
+
268. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007084.png ; $\varepsilon > 0$ ; confidence 1.000
  
−
269. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230116.png ; $- ( - 1 ) ^ { ( q + 1 _ { 1 } - 1 ) ( l _ { 2 } - 1 ) } i ( L _ { 2 } ) \omega \wedge L _ { 1 } , [ \omega \wedge K _ { 1 } , K _ { 2 } ] = \omega \wedge [ K _ { 1 } , K _ { 2 } ] +$ ; confidence 0.276
+
269. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040142.png ; $6$ ; confidence 1.000
  
−
270. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004019.png ; $\| \alpha \| _ { b t } = \| \alpha \| _ { b v } + \sum _ { n = 2 } ^ { \infty } | \sum _ { k = 1 } ^ { n / 2 } \frac { \Delta d _ { n - k } - \Delta d _ { n + k } | } { k }$ ; confidence 0.182
+
270. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001048.png ; $T ^ { - 1 } ( F )$ ; confidence 1.000
  
−
271. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006032.png ; $= \frac { 1 } { z - E _ { 0 } } + \frac { 1 } { z - E _ { 0 } } \int _ { 0 } ^ { \infty } d \lambda ( V \phi | \lambda \rangle \langle \lambda | G ( z ) \phi )$ ; confidence 0.590
+
271. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096030/v09603010.png ; $\epsilon = \mu ^ { - 2 }$ ; confidence 1.000
  
−
272. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010015.png ; $f ( x ) = \frac { 1 } { 4 \pi ^ { 2 } } \int _ { S ^ { 1 } } \int _ { - \infty } ^ { \infty } \frac { \hat { f } _ { p } ( \alpha , p ) } { \alpha x - p } d \alpha d p$ ; confidence 0.166
+
272. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005031.png ; $A ( t )$ ; confidence 1.000
  
−
273. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015059.png ; $\frac { 1 } { 2 ^ { n p / 2 } \Gamma _ { p } ( n / 2 ) | \Sigma | ^ { n / 2 } } | S | ^ { ( n - p - 1 ) / 2 } \operatorname { etr } ( - \frac { 1 } { 2 } \Sigma ^ { - 1 } S )$ ; confidence 0.542
+
273. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005090.png ; $\{ B ( t ) \}$ ; confidence 1.000
  
−
274. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { x } ( \phi ) } { \mu _ { \varepsilon } ^ { x } ( \psi ) }$ ; confidence 0.384
+
274. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120040/v12004011.png ; $\chi ^ { \prime } ( G ) = \Delta ( G )$ ; confidence 1.000
  
−
275. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014026.png ; $f ( x ) = \frac { 1 } { 4 \pi ^ { 2 } } \int _ { S ^ { 1 } } \int _ { - \infty } ^ { \infty } \frac { \hat { f } \rho ( \alpha , p ) } { \alpha x - p } d p d \alpha$ ; confidence 0.340
+
275. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043300/g0433001.png ; $0 < x < \infty$ ; confidence 1.000
  
−
276. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q12007041.png ; $\Delta E = E \otimes g + 1 \otimes E , \epsilon E = 0 , S E = - E g ^ { - 1 } , \Delta F = F \otimes 1 + g ^ { - 1 } \bigotimes F , \epsilon F = 0 , S F = - g F$ ; confidence 0.217
+
276. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031910/d031910156.png ; $f ( z , w )$ ; confidence 1.000
  
−
277. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065043.png ; $\psi _ { n } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) [ \phi _ { n } ( e ^ { i \theta } ) - \phi _ { n } ( z ) ] d \mu ( \theta )$ ; confidence 0.500
+
277. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010070.png ; $\theta _ { 1 } ( 1 , z )$ ; confidence 1.000
  
−
278. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200141.png ; $\geq \frac { 1 } { n } ( \frac { n } { 16 e ( m + n ) } ) ^ { n } \times x _ { k _ { 1 } \leq l _ { 1 } \leq k \leq l _ { 2 } \leq k _ { 2 } } | b _ { 1 } + \ldots + b _ { 2 } |$ ; confidence 0.264
+
278. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016012.png ; $A = R ^ { T } R$ ; confidence 1.000
  
−
279. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008053.png ; $\frac { 1 } { 2 L } \int _ { - L } ^ { L } \phi d t _ { i } = \langle \phi \rangle = ( \frac { 1 } { 2 \pi } ) ^ { 2 g } \int \ldots \int \phi d ^ { 2 g } \theta$ ; confidence 0.788
+
279. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007015.png ; $\frac { \partial } { \partial t } U ( t , s ) - A ( t ) U ( t , s ) = 0$ ; confidence 1.000
  
−
280. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010032.png ; $f ( t ) = \left\{ \begin{array} { l l } { o ( \frac { t } { \operatorname { log } t } ) , } & { d = 2 } \\ { o ( t ) , } & { d \geq 3 } \end{array} \right.$ ; confidence 0.412
+
280. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051014.png ; $g ( F ( u ) )$ ; confidence 1.000
  
−
281. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008046.png ; $- \frac { d } { d s } \operatorname { ln } \alpha ( s ) = - \frac { d } { d L } \operatorname { ln } \frac { f ( L ) } { g ( L ; m , s ) } \frac { d L } { d s } +$ ; confidence 0.993
+
281. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130110/r13011013.png ; $\xi ( s ) = \xi ( 1 - s )$ ; confidence 1.000
  
−
282. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120140/c12014012.png ; $CS ( A ) = \frac { 1 } { 4 \pi } \int _ { M } \operatorname { Tr } ( A \wedge d A + \frac { 2 } { 3 } A \wedge A \wedge A ) \operatorname { mod } 2 \pi$ ; confidence 0.321
+
282. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120260/d12026037.png ; $\alpha _ { k } = \pm 1$ ; confidence 1.000
  
−
283. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120190/d12019025.png ; $\lambda _ { n } ( \Omega ) = \operatorname { inf } \{ \lambda ( L ) : L \subseteq C ^ { \infty } ( \Omega ) , \operatorname { dim } ( L ) = n \}$ ; confidence 0.676
+
283. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010159.png ; $A ( \theta ^ { \prime } , \alpha )$ ; confidence 1.000
  
−
284. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017016.png ; $\lambda _ { k } = \operatorname { sup } \operatorname { inf } \frac { \int _ { \Omega } ( \nabla u ) ^ { 2 } d x } { \int _ { \Omega } u ^ { 2 } d x }$ ; confidence 0.932
+
284. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130340/s13034023.png ; $M = F \times [ 0,1 ]$ ; confidence 1.000
  
−
285. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130090/h13009026.png ; $\langle G \cup \{ t \} : ( \operatorname { ker } ( \tau _ { G } ) ) \cup \{ t ^ { - 1 } \alpha ^ { - 1 } t \mu ( \alpha ) : \forall \alpha \in A \} \}$ ; confidence 0.125
+
285. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m120120115.png ; $A B \in F$ ; confidence 1.000
  
−
286. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110010/h11001028.png ; $\| f \| _ { q } = \{ \operatorname { lim } _ { x \rightarrow \infty } \frac { 1 } { x } \cdot \sum _ { n \leq x } | f ( n ) | ^ { q } \} ^ { 1 / q } < \infty$ ; confidence 0.558
+
286. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090110.png ; $\lambda \in \Lambda ^ { + } ( n , r )$ ; confidence 1.000
  
−
287. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o1300407.png ; $\mu _ { \varepsilon } ^ { x } : = P _ { x } \{ \omega : \rho ( X _ { t } ( \omega ) , \phi ( t ) ) \leq \varepsilon \text { for everyt } \in [ 0 , T ] \}$ ; confidence 0.363
+
287. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030099.png ; $B ( m , n , i - 1 )$ ; confidence 1.000
  
−
288. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014040.png ; $| f _ { \rho } ^ { C } ( x _ { 0 } ) - \frac { f + ( x _ { 0 } ) + f - ( x _ { 0 } ) } { 2 } | = O ( \rho \operatorname { ln } \rho ) \text { as } \rho \rightarrow 0$ ; confidence 0.684
+
288. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130060/c13006027.png ; $A = A ( \Gamma )$ ; confidence 1.000
  
−
289. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041059.png ; $\frac { Q _ { n } ( z ) } { P _ { n } ^ { \langle \alpha , \beta \rangle } ( z ) } \stackrel { 2 } { \rightarrow } \frac { 2 } { \phi ^ { \prime } ( z ) }$ ; confidence 0.087
+
289. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130080/z1300805.png ; $p ( x , y )$ ; confidence 1.000
  
−
290. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200171.png ; $A = \frac { 1 } { 6 n 16 ^ { N } } ( \frac { 1 + \rho } { 2 } ) ^ { m } ( \frac { 1 - \rho } { 2 } ) ^ { 2 n + k } | \operatorname { Re } \sum _ { j = 1 } ^ { n } b _ { j } |$ ; confidence 0.618
+
290. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840158.png ; $A = A ^ { + }$ ; confidence 1.000
  
−
291. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018081.png ; $\xi ( t ) = \frac { 1 } { \sqrt { \omega _ { N + 1 } } } \int _ { R ^ { N } } \frac { e ^ { i ( t , \lambda ) } - 1 } { | \lambda | ^ { ( N + 1 ) / 2 } } W ( d \lambda )$ ; confidence 0.882
+
291. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010520/a01052066.png ; $y ^ { \prime } = f ( x , y )$ ; confidence 1.000
  
−
292. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013079.png ; $F _ { j k } ^ { ( l ) } : = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau _ { l } )$ ; confidence 0.981
+
292. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900170.png ; $g ( \zeta ) = T ( \zeta ) f ( \zeta )$ ; confidence 1.000
  
−
293. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004054.png ; $p _ { X } = \operatorname { lim } _ { s \rightarrow \infty } \frac { \operatorname { log } s } { \operatorname { log } \| D _ { s } \| _ { X } }$ ; confidence 0.848
+
293. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001041.png ; $f ( x ) \in L ^ { 2 } ( D ^ { \prime } )$ ; confidence 1.000
  
−
294. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043046.png ; $\left.\begin{array} { l } { n } \\ { m } \end{array} \right] _ { q } = \frac { [ n ] q ! } { [ m ] q ! [ n - m ] q ! } , [ m ] q = \frac { 1 - q ^ { m } } { 1 - q }$ ; confidence 0.404
+
294. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520189.png ; $A ^ { T } = - A$ ; confidence 1.000
  
−
295. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004059.png ; $\sigma = \frac { ( n - 1 ) ! } { ( 2 \pi i ) ^ { n } } \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } \rho ^ { \prime } d \rho ^ { \prime } [ j ] \wedge \alpha \zeta$ ; confidence 0.658
+
295. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120140/f12014021.png ; $\lambda = \infty$ ; confidence 1.000
  
−
296. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007015.png ; $\sum _ { i < n + 1 } ( - 1 ) ^ { n + 1 - i } \operatorname { pr } ( \alpha _ { 1 } , \ldots , \alpha _ { i + 1 } \alpha _ { i } , \ldots , \alpha _ { n + 1 } ) +$ ; confidence 0.229
+
296. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005070.png ; $\frac { d u ( t ) } { d t } + A ( t ) u ( t ) = f ( t )$ ; confidence 1.000
  
−
297. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016047.png ; $J ^ { \prime } = \left( \begin{array} { c c } { f \omega ^ { 2 } - f ^ { - 1 } r ^ { 2 } } & { - f \omega } \\ { - f \omega } & { f } \end{array} \right)$ ; confidence 0.976
+
297. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n120020103.png ; $( \operatorname { cos } t ) ^ { - 1 }$ ; confidence 1.000
  
−
298. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023075.png ; $E ^ { \vec { \alpha } } ( L ) = \frac { \partial L } { \partial y ^ { \alpha } } - D _ { i } ( \frac { \partial L } { \partial y ^ { \alpha _ { i } } } )$ ; confidence 0.068
+
298. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008019.png ; $\forall f \in H$ ; confidence 1.000
  
−
299. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f11001021.png ; $\operatorname { inf } ( x , y ) = 0 \Rightarrow \operatorname { inf } ( z x , y ) = \operatorname { inf } ( x z , y ) = 0 , \forall z \in A ^ { + }$ ; confidence 0.909
+
299. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180176.png ; $\{ p , q , r , s \}$ ; confidence 1.000
  
−
300. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049012.png ; $\frac { 2 \nu ^ { 2 } \frac { 2 } { 2 } ( \nu _ { 1 } + \nu _ { 2 } - 2 ) } { \nu _ { 1 } ( \nu _ { 2 } - 2 ) ^ { 2 } ( \nu _ { 2 } - 4 ) } \quad \text { for } \nu _ { 2 } > 4$ ; confidence 0.199
+
300. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180175.png ; $\{ p , q \}$ ; confidence 1.000

Revision as of 00:10, 13 February 2020

List

1. s130620191.png ; $\sqrt { x }$ ; confidence 1.000

2. f130090107.png ; $( r - 1 )$ ; confidence 1.000

3. t12007034.png ; $196883 + 1$ ; confidence 1.000

4. g130050109.png ; $( d + 1 )$ ; confidence 1.000

5. c0268508.png ; $f , g$ ; confidence 1.000

6. l120170241.png ; $T ( 4 )$ ; confidence 1.000

7. c1300703.png ; $f ( X , Y ) = 0$ ; confidence 1.000

8. h12004033.png ; $G ( \omega , \omega )$ ; confidence 1.000

9. c120180203.png ; $0 < p \leq 4$ ; confidence 1.000

10. m13026035.png ; $( \lambda , \rho )$ ; confidence 1.000

11. d12030024.png ; $\gamma ( X ( t ) )$ ; confidence 1.000

12. a01022084.png ; $p > 3$ ; confidence 1.000

13. t12006029.png ; $\int \rho = N$ ; confidence 1.000

14. e120260122.png ; $B ( n , p )$ ; confidence 1.000

15. f12021047.png ; $u ( z , \lambda )$ ; confidence 1.000

16. a01233047.png ; $f ^ { - 1 } ( y )$ ; confidence 1.000

17. c02318027.png ; $2 n - 2$ ; confidence 1.000

18. z1200209.png ; $71 = 55 + 13 + 3$ ; confidence 1.000

19. a01297086.png ; $p ^ { \prime } = p / ( p - 1 )$ ; confidence 1.000

20. a12005037.png ; $\rho ( A ( t ) )$ ; confidence 1.000

21. b13019045.png ; $\alpha = 1 / 2$ ; confidence 1.000

22. f13016054.png ; $\mu ( M , P )$ ; confidence 1.000

23. m13002035.png ; $( k - 1 ) ^ { 2 }$ ; confidence 1.000

24. z12002048.png ; $21 + 8 + 2 = 31$ ; confidence 1.000

25. e12023052.png ; $0 = f ^ { \prime } ( 0 ) =$ ; confidence 1.000

26. v13007058.png ; $\theta ( 0 ) = 0$ ; confidence 1.000

27. l12009078.png ; $A \times \{ 0 \}$ ; confidence 1.000

28. d03071014.png ; $4 \pi$ ; confidence 1.000

29. b120150103.png ; $B ( n , 1 / 2 )$ ; confidence 1.000

30. c11016038.png ; $[ 0,1 ]$ ; confidence 1.000

31. v13007061.png ; $q ( 1 ) = 0$ ; confidence 1.000

32. a12005073.png ; $D ( A ( t ) )$ ; confidence 1.000

33. i12001018.png ; $\sigma ( 0 ) = 0$ ; confidence 1.000

34. t12005039.png ; $i ( p - n + i )$ ; confidence 1.000

35. a13002015.png ; $\mu ( A ) = 0$ ; confidence 1.000

36. b13011026.png ; $\{ p ( t ) : 0 \leq t \leq 1 \}$ ; confidence 1.000

37. t13011034.png ; $( T , - )$ ; confidence 1.000

38. a011600224.png ; $( \alpha , \beta )$ ; confidence 1.000

39. b0159504.png ; $B ( m , n )$ ; confidence 1.000

40. s13041060.png ; $\phi ( z ) = z + \sqrt { z ^ { 2 } - 1 }$ ; confidence 1.000

41. a0136105.png ; $- \infty$ ; confidence 1.000

42. a01246093.png ; $f ( t , x )$ ; confidence 1.000

43. a12008067.png ; $A ( t ) ^ { 1 / 2 }$ ; confidence 1.000

44. b12027031.png ; $F ( 0 ) = 0$ ; confidence 1.000

45. b12024012.png ; $\{ \infty \}$ ; confidence 1.000

46. d033210100.png ; $\lambda = ( \lambda _ { 1 } , \lambda _ { 2 } )$ ; confidence 1.000

47. i13001019.png ; $\operatorname { sgn } ( \sigma ) = 1$ ; confidence 1.000

48. b12002021.png ; $t \in ( 0,1 )$ ; confidence 1.000

49. e03701037.png ; $T ( A )$ ; confidence 1.000

50. d0302404.png ; $| t | < \delta$ ; confidence 1.000

51. a13007029.png ; $b = 5$ ; confidence 1.000

52. a013180166.png ; $( k - 1 )$ ; confidence 1.000

53. m13007017.png ; $p ^ { 2 } = m ^ { 2 }$ ; confidence 1.000

54. s120230150.png ; $A ^ { 2 } = A$ ; confidence 1.000

55. s12020066.png ; $\operatorname { sgn } ( \pi )$ ; confidence 1.000

56. c13016050.png ; $s ( n ) \geq \operatorname { log } n$ ; confidence 1.000

57. t120070116.png ; $J ( z ) =$ ; confidence 1.000

58. w12021063.png ; $( 1,1,1,1 , R ) = ( 1,4 , R )$ ; confidence 1.000

59. l0600408.png ; $f ( z ) = 0$ ; confidence 1.000

60. m13001043.png ; $R ( i )$ ; confidence 1.000

61. h12011033.png ; $\Gamma \subseteq B ( 0,1 )$ ; confidence 1.000

62. r12002010.png ; $g ( q )$ ; confidence 1.000

63. e1201202.png ; $f ( \theta , \phi )$ ; confidence 1.000

64. s12004052.png ; $\lambda ^ { \prime } = ( 3,2,1,1 )$ ; confidence 1.000

65. s130510106.png ; $\gamma ( F ( u ) ) = K$ ; confidence 1.000

66. r13014023.png ; $\sigma ( T ) = \{ 0 \}$ ; confidence 1.000

67. g13005023.png ; $r ( 1,2 ) = 6$ ; confidence 1.000

68. a0137508.png ; $A , B$ ; confidence 1.000

69. e12026013.png ; $D ( \mu )$ ; confidence 1.000

70. g13005056.png ; $2 d - 1$ ; confidence 1.000

71. i05032047.png ; $f ( y ) = 0$ ; confidence 1.000

72. l06003075.png ; $\sigma = \pi - A - B - C$ ; confidence 1.000

73. k12012039.png ; $[ - 1 / 2 , + \infty ]$ ; confidence 1.000

74. a12007075.png ; $\eta \in ( 0,1 ]$ ; confidence 1.000

75. a12007071.png ; $\rho \in ( 0,1 ]$ ; confidence 1.000

76. b13022084.png ; $F ( u ) = 0$ ; confidence 1.000

77. l13006053.png ; $V ( f )$ ; confidence 1.000

78. c120010175.png ; $A ( E ) \rightarrow A ( E )$ ; confidence 1.000

79. f12008042.png ; $\varphi = ( \xi , \eta )$ ; confidence 1.000

80. m06222052.png ; $( n , n , n ) ^ { 2 }$ ; confidence 1.000

81. n067520280.png ; $- \infty < \xi < \infty$ ; confidence 1.000

82. c022660151.png ; $E = 0$ ; confidence 1.000

83. b130120103.png ; $p \in [ 1,2 ]$ ; confidence 1.000

84. z1301209.png ; $p ( \xi ) = \eta$ ; confidence 1.000

85. a01197078.png ; $2 \pi$ ; confidence 1.000

86. c02514022.png ; $[ 0 , t ]$ ; confidence 1.000

87. b12020063.png ; $U ( m , n )$ ; confidence 1.000

88. a120180103.png ; $F ^ { \prime } ( x ) \neq 1$ ; confidence 1.000

89. w0975906.png ; $H ^ { 1 } ( k , A )$ ; confidence 1.000

90. s12034085.png ; $u ( D ^ { 2 } )$ ; confidence 1.000

91. b120400127.png ; $w ( p - \delta ) + \delta$ ; confidence 1.000

92. h12004032.png ; $\xi < \lambda$ ; confidence 1.000

93. c130070191.png ; $R ^ { \prime } ( P ) = R ( P )$ ; confidence 1.000

94. z13010023.png ; $( \varphi \rightarrow \psi )$ ; confidence 1.000

95. p13007092.png ; $G ( z , w )$ ; confidence 1.000

96. a12005056.png ; $\alpha \in ( 0,1 ]$ ; confidence 1.000

97. m130180155.png ; $\phi ( G ; s )$ ; confidence 1.000

98. g130040156.png ; $\Omega \times G ( n , m )$ ; confidence 1.000

99. d12029029.png ; $f ( q ) = 0$ ; confidence 1.000

100. a01012059.png ; $b > 0$ ; confidence 1.000

101. f12019078.png ; $\{ 1 \} < N < G$ ; confidence 1.000

102. n120020114.png ; $2 d + 4$ ; confidence 1.000

103. p13009042.png ; $\eta \in \partial \Omega$ ; confidence 1.000

104. c02514043.png ; $t \in [ 0,1 ]$ ; confidence 1.000

105. z13003052.png ; $Q = [ 0,1 ] \times [ 0,1 ]$ ; confidence 1.000

106. m0655301.png ; $[ - \pi , \pi )$ ; confidence 1.000

107. a01058026.png ; $( k + 1 )$ ; confidence 1.000

108. a01046080.png ; $f ( x )$ ; confidence 1.000

109. m1302003.png ; $\{ f , g \} = P ( d f , d g )$ ; confidence 1.000

110. f1201503.png ; $B ( X , Y )$ ; confidence 1.000

111. m12010032.png ; $\sigma ( y )$ ; confidence 1.000

112. m120130127.png ; $\lambda - \delta \xi > 0$ ; confidence 1.000

113. s09082025.png ; $\sigma ( X , Y )$ ; confidence 1.000

114. p07251032.png ; $\mu \neq 0$ ; confidence 1.000

115. c13014019.png ; $A , B \in W$ ; confidence 1.000

116. j12002074.png ; $\{ T = \infty \}$ ; confidence 1.000

117. m13008017.png ; $p = ( 1,1,00 )$ ; confidence 1.000

118. b13030077.png ; $2 ^ { 9 }$ ; confidence 1.000

119. w12021031.png ; $m = 35$ ; confidence 1.000

120. b13021034.png ; $g + g ^ { T }$ ; confidence 1.000

121. c13010046.png ; $\alpha \in [ 0 , + \infty ]$ ; confidence 1.000

122. l12006015.png ; $G ( z ) = ( z - H ) ^ { - 1 }$ ; confidence 1.000

123. n067520195.png ; $A ^ { T } = A$ ; confidence 1.000

124. f12024036.png ; $h ( t ) \geq 0$ ; confidence 1.000

125. t1300705.png ; $\rho ( \tau )$ ; confidence 1.000

126. h12004013.png ; $G ( \kappa , \lambda )$ ; confidence 1.000

127. g130050105.png ; $( d - 1 )$ ; confidence 1.000

128. w12007027.png ; $( p , q , t ) ( p ^ { \prime } , q ^ { \prime } , t ^ { \prime } ) =$ ; confidence 1.000

129. l0600303.png ; $B ^ { \prime } B$ ; confidence 1.000

130. j120020103.png ; $\gamma \in ( 0 , \infty )$ ; confidence 1.000

131. s12025038.png ; $\lambda \in [ 0,2 ]$ ; confidence 1.000

132. e120140102.png ; $( 1 \rightarrow \varphi ) = \varphi$ ; confidence 1.000

133. d12023089.png ; $\{ x , y \}$ ; confidence 1.000

134. w13013053.png ; $W = 2 \pi ^ { 2 }$ ; confidence 1.000

135. d12005059.png ; $f ( E )$ ; confidence 1.000

136. p1201207.png ; $g ^ { \prime }$ ; confidence 1.000

137. w12018077.png ; $\xi ( t ) - \xi ( s )$ ; confidence 1.000

138. k13001040.png ; $t = A ^ { - 4 }$ ; confidence 1.000

139. p075660111.png ; $| \xi | \geq 1$ ; confidence 1.000

140. a12017033.png ; $= 0$ ; confidence 1.000

141. e13004027.png ; $U ( t ) = U _ { 0 } ( t )$ ; confidence 1.000

142. c02280056.png ; $1$ ; confidence 1.000

143. d03024010.png ; $\gamma ( 0 ) = 0$ ; confidence 1.000

144. m1201606.png ; $( p \times n )$ ; confidence 1.000

145. b11066069.png ; $T ( 1 )$ ; confidence 1.000

146. e13007049.png ; $f ( x + h ) - f ( x )$ ; confidence 1.000

147. m12016031.png ; $( q \times n )$ ; confidence 1.000

148. x1200309.png ; $( \theta , p )$ ; confidence 1.000

149. d03165025.png ; $f _ { 1 } = f$ ; confidence 1.000

150. b110630108.png ; $R G$ ; confidence 1.000

151. s130510131.png ; $\gamma ( w ) = \gamma ( u )$ ; confidence 1.000

152. f13029072.png ; $( Y , \sigma )$ ; confidence 1.000

153. m12011059.png ; $M = T ( h )$ ; confidence 1.000

154. p12012024.png ; $1$ ; confidence 1.000

155. b12015073.png ; $p \in [ 0,1 ]$ ; confidence 1.000

156. h04632090.png ; $G ( z )$ ; confidence 1.000

157. n066630125.png ; $\rho > 1 / 2$ ; confidence 1.000

158. h12002076.png ; $\phi - f$ ; confidence 1.000

159. e12014022.png ; $\rho ( f ) = 0$ ; confidence 1.000

160. c12017036.png ; $\beta _ { 0 } > 0$ ; confidence 1.000

161. m12007056.png ; $x ^ { 3 } - x - 1$ ; confidence 1.000

162. n1200409.png ; $G M$ ; confidence 1.000

163. t12020064.png ; $| z _ { j } | = 1$ ; confidence 1.000

164. w13008090.png ; $g = N - 1$ ; confidence 1.000

165. s13051047.png ; $G = ( V , U )$ ; confidence 1.000

166. v13007054.png ; $\theta ^ { \prime } = \theta - \pi$ ; confidence 1.000

167. z13012032.png ; $\xi \in ( - 1,1 )$ ; confidence 1.000

168. b12001030.png ; $u ( \xi , \eta ) = 0$ ; confidence 1.000

169. b13022055.png ; $F ( q ) = 0$ ; confidence 1.000

170. l06105016.png ; $f ( P ) > 0$ ; confidence 1.000

171. o13006065.png ; $p ( \lambda _ { 1 } , \lambda _ { 2 } ) = 0$ ; confidence 1.000

172. k12012018.png ; $f ( x ) > 0$ ; confidence 1.000

173. p130070120.png ; $\delta ( z , w )$ ; confidence 1.000

174. b12009056.png ; $f ( z ) =$ ; confidence 1.000

175. g13005097.png ; $( d - 2 )$ ; confidence 1.000

176. c12001041.png ; $T ( E )$ ; confidence 1.000

177. d12018023.png ; $\frac { 1 } { 2 \pi } d \theta$ ; confidence 1.000

178. i13006074.png ; $A = A ( x , y )$ ; confidence 1.000

179. a13004020.png ; $\varphi \in \Gamma$ ; confidence 1.000

180. a11016010.png ; $O ( n ^ { 3 } )$ ; confidence 1.000

181. t12005015.png ; $( n - i + 1 ) \times ( n - i + 1 )$ ; confidence 1.000

182. w120110271.png ; $| \xi | > 1$ ; confidence 1.000

183. b13022013.png ; $\rho = \rho ( T ) = \operatorname { diam } ( T )$ ; confidence 1.000

184. b13028047.png ; $[ T ( n ) , X ]$ ; confidence 1.000

185. s120230149.png ; $( n - k ) / 2$ ; confidence 1.000

186. p12012038.png ; $( 6 \times 6 )$ ; confidence 1.000

187. c02583062.png ; $\{ T ( s ) \}$ ; confidence 1.000

188. m12001029.png ; $p \in ( 0 , \infty )$ ; confidence 1.000

189. f12015047.png ; $i ( A ^ { \prime } ) = - i ( A )$ ; confidence 1.000

190. f120080199.png ; $A ( K ) = A ( G )$ ; confidence 1.000

191. s130540102.png ; $( \infty \times \infty )$ ; confidence 1.000

192. i13009072.png ; $0 \leq i \leq n - 1$ ; confidence 1.000

193. b120040162.png ; $1 < p < 2$ ; confidence 1.000

194. e12020022.png ; $( 1 + \epsilon )$ ; confidence 1.000

195. e12006034.png ; $\Gamma ( y )$ ; confidence 1.000

196. l1300605.png ; $[ 0,1 )$ ; confidence 1.000

197. a01052024.png ; $f ( n )$ ; confidence 1.000

198. b11039063.png ; $A ( x , y )$ ; confidence 1.000

199. f12016053.png ; $T = T _ { 1 } + K$ ; confidence 1.000

200. h04632097.png ; $f ( z ) \in H ^ { 1 }$ ; confidence 1.000

201. f12021019.png ; $z = u ^ { \lambda }$ ; confidence 1.000

202. f120080113.png ; $B ( X , X )$ ; confidence 1.000

203. c130070130.png ; $f ( X , Y )$ ; confidence 1.000

204. c13007041.png ; $n ( n - 2 ) - ( n - 1 ) ( n - 2 ) = n - 2$ ; confidence 1.000

205. a12010049.png ; $\lambda > 0$ ; confidence 1.000

206. d12014059.png ; $( n , 6 ) = 1$ ; confidence 1.000

207. t12020076.png ; $[ \sqrt { n } , \sqrt { n + 1 } ]$ ; confidence 1.000

208. z13001053.png ; $x ( 1 ) = 0$ ; confidence 1.000

209. m120030108.png ; $\int \rho ( u ) d \Phi ( u )$ ; confidence 1.000

210. z12001086.png ; $( 3 m - 2 )$ ; confidence 1.000

211. z13007011.png ; $\pm g$ ; confidence 1.000

212. z13001054.png ; $x ( 2 ) = 1$ ; confidence 1.000

213. a13017034.png ; $( n - 1 )$ ; confidence 1.000

214. x12003010.png ; $( - \theta , - p )$ ; confidence 1.000

215. i12004090.png ; $( n , n - q - 1 )$ ; confidence 1.000

216. s13065027.png ; $\delta _ { \mu } > 0$ ; confidence 1.000

217. b12006020.png ; $\epsilon = - 1$ ; confidence 1.000

218. b13019011.png ; $f ( m )$ ; confidence 1.000

219. a01160064.png ; $p > 2$ ; confidence 1.000

220. v09690078.png ; $\phi ( T ) < \infty$ ; confidence 1.000

221. b01514018.png ; $f ^ { - 1 } ( 0 )$ ; confidence 1.000

222. e03572015.png ; $f ( 0 ) \neq 0$ ; confidence 1.000

223. a011490110.png ; $p > 0$ ; confidence 1.000

224. w13007030.png ; $( \beta _ { k } | \beta _ { k } ) = 0$ ; confidence 1.000

225. f13024057.png ; $( \varepsilon , \delta )$ ; confidence 1.000

226. l12010039.png ; $\gamma \geq \Gamma$ ; confidence 1.000

227. h12011024.png ; $B ( 0 , r )$ ; confidence 1.000

228. s13065016.png ; $H ( 0 ) = 1$ ; confidence 1.000

229. q12002040.png ; $\{ \lambda _ { 1 } , \lambda _ { 2 } \}$ ; confidence 1.000

230. a12007014.png ; $U ( t , s ) , 0 \leq s \leq t \leq T$ ; confidence 1.000

231. w11006020.png ; $C = C [ 0 , \infty )$ ; confidence 1.000

232. a13024014.png ; $N ( 0 , \sigma ^ { 2 } )$ ; confidence 1.000

233. o130060128.png ; $f ( \lambda _ { 1 } , \lambda _ { 2 } ) = 0$ ; confidence 1.000

234. m130140120.png ; $( n ^ { 2 } \times n ^ { 2 } )$ ; confidence 1.000

235. h046010153.png ; $T ^ { 4 } \times [ 0,1 ]$ ; confidence 1.000

236. e120120120.png ; $f ( \theta , \phi , \alpha )$ ; confidence 1.000

237. a13007088.png ; $\operatorname { log } \operatorname { log } n ) ^ { 3 }$ ; confidence 1.000

238. z12001044.png ; $t \neq 0,1$ ; confidence 1.000

239. m11011025.png ; $p + q < 2 ( m + n )$ ; confidence 1.000

240. f0401407.png ; $\alpha < \beta$ ; confidence 1.000

241. a1300803.png ; $f ( x ) \leq h ( x )$ ; confidence 1.000

242. z13007016.png ; $u = \pm x ^ { - 1 } g x$ ; confidence 1.000

243. a12006018.png ; $b ( x )$ ; confidence 1.000

244. l12008016.png ; $( 0 , y )$ ; confidence 1.000

245. t12003044.png ; $E ^ { \prime } = f ( E )$ ; confidence 1.000

246. e13007053.png ; $f ^ { \prime } ( N ) = B$ ; confidence 1.000

247. b13018018.png ; $0 < R < \infty$ ; confidence 1.000

248. a0138205.png ; $g ( P )$ ; confidence 1.000

249. w120090163.png ; $\Delta ( \lambda ) ^ { \perp }$ ; confidence 1.000

250. s086520149.png ; $\phi ( T ) = 0$ ; confidence 1.000

251. h12007031.png ; $( n - k - 1 )$ ; confidence 1.000

252. d03289086.png ; $0 < \sigma < 1$ ; confidence 1.000

253. b11022075.png ; $i ^ { 2 } = - 1$ ; confidence 1.000

254. k13002044.png ; $\operatorname { sign } ( Y _ { 1 } - Y _ { 2 } )$ ; confidence 1.000

255. o1100106.png ; $P ( G ) \cup P ( G ) ^ { - 1 } = G$ ; confidence 1.000

256. i13006040.png ; $f ^ { \prime } ( 0 ) \neq 0$ ; confidence 1.000

257. b12034034.png ; $D = U _ { 1 }$ ; confidence 1.000

258. a01300080.png ; $P ( z )$ ; confidence 1.000

259. d12029014.png ; $f ( q ) = 1 / q ^ { 2 }$ ; confidence 1.000

260. f120230105.png ; $( \omega \wedge D ) \varphi = \omega \wedge D ( \varphi )$ ; confidence 1.000

261. t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000

262. n13005048.png ; $( s , r + 1 )$ ; confidence 1.000

263. j13007017.png ; $\Gamma ( \omega , \alpha )$ ; confidence 1.000

264. h12015035.png ; $G ( \phi )$ ; confidence 1.000

265. c02412037.png ; $\sigma > 1$ ; confidence 1.000

266. w120090149.png ; $\Delta ( \lambda )$ ; confidence 1.000

267. m12009038.png ; $P ( \xi ) = 0$ ; confidence 1.000

268. a13007084.png ; $\varepsilon > 0$ ; confidence 1.000

269. a110040142.png ; $6$ ; confidence 1.000

270. c12001048.png ; $T ^ { - 1 } ( F )$ ; confidence 1.000

271. v09603010.png ; $\epsilon = \mu ^ { - 2 }$ ; confidence 1.000

272. a12005031.png ; $A ( t )$ ; confidence 1.000

273. a12005090.png ; $\{ B ( t ) \}$ ; confidence 1.000

274. v12004011.png ; $\chi ^ { \prime } ( G ) = \Delta ( G )$ ; confidence 1.000

275. g0433001.png ; $0 < x < \infty$ ; confidence 1.000

276. d031910156.png ; $f ( z , w )$ ; confidence 1.000

277. f12010070.png ; $\theta _ { 1 } ( 1 , z )$ ; confidence 1.000

278. c12016012.png ; $A = R ^ { T } R$ ; confidence 1.000

279. a12007015.png ; $\frac { \partial } { \partial t } U ( t , s ) - A ( t ) U ( t , s ) = 0$ ; confidence 1.000

280. s13051014.png ; $g ( F ( u ) )$ ; confidence 1.000

281. r13011013.png ; $\xi ( s ) = \xi ( 1 - s )$ ; confidence 1.000

282. d12026037.png ; $\alpha _ { k } = \pm 1$ ; confidence 1.000

283. o130010159.png ; $A ( \theta ^ { \prime } , \alpha )$ ; confidence 1.000

284. s13034023.png ; $M = F \times [ 0,1 ]$ ; confidence 1.000

285. m120120115.png ; $A B \in F$ ; confidence 1.000

286. w120090110.png ; $\lambda \in \Lambda ^ { + } ( n , r )$ ; confidence 1.000

287. b13030099.png ; $B ( m , n , i - 1 )$ ; confidence 1.000

288. c13006027.png ; $A = A ( \Gamma )$ ; confidence 1.000

289. z1300805.png ; $p ( x , y )$ ; confidence 1.000

290. k055840158.png ; $A = A ^ { + }$ ; confidence 1.000

291. a01052066.png ; $y ^ { \prime } = f ( x , y )$ ; confidence 1.000

292. v096900170.png ; $g ( \zeta ) = T ( \zeta ) f ( \zeta )$ ; confidence 1.000

293. o13001041.png ; $f ( x ) \in L ^ { 2 } ( D ^ { \prime } )$ ; confidence 1.000

294. n067520189.png ; $A ^ { T } = - A$ ; confidence 1.000

295. f12014021.png ; $\lambda = \infty$ ; confidence 1.000

296. a12005070.png ; $\frac { d u ( t ) } { d t } + A ( t ) u ( t ) = f ( t )$ ; confidence 1.000

297. n120020103.png ; $( \operatorname { cos } t ) ^ { - 1 }$ ; confidence 1.000

298. r13008019.png ; $\forall f \in H$ ; confidence 1.000

299. c120180176.png ; $\{ p , q , r , s \}$ ; confidence 1.000

300. c120180175.png ; $\{ p , q \}$ ; confidence 1.000

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/2&oldid=44412
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