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User:Maximilian Janisch/latexlist/latex/NoNroff/6

From Encyclopedia of Mathematics
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1. z13008049.png ; $= - n ( n + 2 + 2 \alpha ) f , D = z \frac { \partial } { \partial z } + z \frac { \partial } { \partial z }$ ; confidence 0.987

2. a13013028.png ; $\phi _ { - } ( x , t , z ) = \operatorname { exp } ( \sum _ { i = 1 } ^ { \infty } \chi _ { i } ( x , t ) z ^ { - i } )$ ; confidence 0.963

3. a130040754.png ; $_ { R } , \mathfrak { M } ( r ) = \operatorname { mng } _ { P \cup R } , \mathfrak { M } ( \varphi _ { r } )$ ; confidence 0.815

4. a12007095.png ; $\frac { \partial u } { \partial t } = L ( t , x , D _ { x } ) u + f ( t , x ) \text { in } [ 0 , T ] \times \Omega$ ; confidence 0.831

5. a130060102.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { P ^ { \# } ( n ) } { G ^ { \# } ( n ) } = \lambda$ ; confidence 0.751

6. a13008050.png ; $\frac { d \operatorname { ln } g ( L ; m , s ) } { d m } \frac { d \operatorname { ln } g ( R ; m , s ) } { d s }$ ; confidence 0.495

7. a1103208.png ; $+ h \sum _ { j = 1 } ^ { i - 1 } A _ { j } ( h T ) [ f ( t _ { m } + c _ { j } h , u _ { m + 1 } ^ { ( j ) } ) - T u _ { n j } ^ { ( j ) } + 1 ]$ ; confidence 0.207

8. a12016070.png ; $S _ { t } = \omega ( 1 - \lambda ) + \lambda S _ { t - 1 } + c _ { 1 } u _ { t } + \mu _ { t } - \lambda \mu _ { t - 1 }$ ; confidence 0.412

9. a13032042.png ; $E _ { \theta } ( N ) = \frac { P _ { \theta } ( S _ { N } = K ) K - P _ { \theta } ( S _ { N } = - J ) J } { 2 \theta - 1 }$ ; confidence 0.641

10. b11066014.png ; $\| f \| _ { * } = \operatorname { sup } _ { Q } \frac { 1 } { | Q | } \int _ { Q } | f ( t ) - f _ { Q } | d t < \infty$ ; confidence 0.901

11. b12009037.png ; $( 1 + \alpha ^ { 2 } ) \frac { d \tau } { \tau } = ( p _ { S } ( \xi , \tau ) - \alpha i ) \frac { d \xi } { \xi }$ ; confidence 0.647

12. b1201609.png ; $x _ { j } ^ { \prime } = \sum _ { i , k } p _ { i k } , j _ { i } x _ { k } , \quad x _ { i } \geq 0 , \sum _ { i } x _ { i } = 1$ ; confidence 0.343

13. b12051059.png ; $H _ { + } = H _ { c } + \frac { y y ^ { T } } { y ^ { T } s } - \frac { ( H _ { c } s ) ( H _ { c } s ) ^ { T } } { s ^ { T } H _ { c } s }$ ; confidence 0.956

14. c13016061.png ; $\operatorname { lim } _ { n \rightarrow \infty } t ( n ) ( \operatorname { log } t ( n ) ) / s ( n ) = 0$ ; confidence 0.906

15. c120180159.png ; $g ^ { - 1 } ( \theta \otimes \varphi ) = \langle \theta , \gamma ^ { - 1 } ( \varphi ) \rangle \in R$ ; confidence 0.653

16. c120180240.png ; $g ^ { - 1 } \{ p _ { 1 } , p _ { 2 } ; \ldots ; p _ { 4 m - 1 } , p _ { 4 m } \} ( W ( g ) \otimes \ldots \otimes W ( g ) )$ ; confidence 0.422

17. d12023064.png ; $= \sum _ { i = 0 } ^ { p - 1 } L ( x _ { i } ) L ^ { * } ( x _ { i } ) - \sum _ { i = 0 } ^ { q - 1 } L ( y _ { i } ) L ^ { * } ( y _ { i } )$ ; confidence 0.584

18. e12012065.png ; $\propto \| \Sigma \| ^ { - 1 / 2 } [ \nu + ( y - \mu ) ^ { T } \Sigma ^ { - 1 } ( y - \mu ) ] ^ { - ( \nu + p ) / 2 }$ ; confidence 0.904

19. e03500092.png ; $H _ { \epsilon } ^ { \prime \prime } ( X ) = \operatorname { inf } \{ H ( U ) : U \in A _ { \epsilon } \}$ ; confidence 0.867

20. e12023058.png ; $E ( L ) = \frac { \partial L } { \partial y } - D ( \frac { \partial L } { \partial y ^ { \prime } } )$ ; confidence 0.989

21. f1300909.png ; $\alpha ( x ) = \frac { x + ( x ^ { 2 } + 4 ) ^ { 1 / 2 } } { 2 } , \beta ( x ) = \frac { x - ( x ^ { 2 } + 4 ) ^ { 1 / 2 } } { 2 }$ ; confidence 0.989

22. f130100137.png ; $T = c _ { 1 } \lambda ^ { p } ( \delta _ { x _ { 1 } } ) + \ldots + c _ { n } \lambda ^ { p } ( \delta _ { x _ { n } } )$ ; confidence 0.835

23. f12009037.png ; $| f ( \zeta ) | \leq C _ { \epsilon } \operatorname { exp } ( H _ { K } ( \zeta ) + \epsilon | \zeta | )$ ; confidence 0.990

24. f13024045.png ; $\left( \begin{array} { r r } { 0 } & { 0 } \\ { - \varepsilon K ( c , d ) } & { 0 } \end{array} \right)$ ; confidence 0.448

25. g130040141.png ; $F _ { K } ( S _ { 1 } , S _ { 2 } ) = \operatorname { inf } \{ M ( U ) + M ( V ) : U + \partial V = S _ { 1 } - S _ { 2 } \}$ ; confidence 0.655

26. g12004083.png ; $\Sigma _ { P } = \{ ( x , \xi ) \in \Omega \times ( R ^ { n } \backslash \{ 0 \} ) : p _ { m } ( x , \xi ) = 0 \}$ ; confidence 0.632

27. h1100101.png ; $M ( f ) = \operatorname { lim } _ { x \rightarrow \infty } \frac { 1 } { x } \cdot \sum _ { n < x } f ( n )$ ; confidence 0.532

28. h12011040.png ; $S _ { n + 1 } = \{ z \in C ^ { n + 1 } : \operatorname { Im } z _ { n + 1 } > \sum ^ { n _ { j = 1 } } | z _ { j } | ^ { 2 } \}$ ; confidence 0.163

29. i130030181.png ; $\phi _ { * } ( \text { ind } ( D ) ) = ( - 1 ) ^ { n } ( 2 \pi i ) ^ { - m } ( Ch ( [ a ] ) T ( M ) f ^ { * } \phi ) [ T ^ { * } M ]$ ; confidence 0.164

30. i1300408.png ; $bv = \{ d = \{ d _ { k } \} : \| \alpha \| _ { bv } = \sum _ { k = 0 } ^ { \infty } | \Delta d _ { k } | < \infty \}$ ; confidence 0.358

31. i1200407.png ; $b _ { 0 } P = \{ ( \zeta _ { 1 } , \dots , \zeta _ { n } ) : | \zeta _ { j } - a _ { j } | = r _ { j } , j = 1 , \dots , n \}$ ; confidence 0.718

32. i13005068.png ; $S : = \{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J , k _ { j } > 0 , m _ { j } ^ { + } > 0 , k > 0 \}$ ; confidence 0.873

33. i130060172.png ; $+ \int _ { \frac { x + y } { 2 } } ^ { \infty } d s \int _ { 0 } ^ { \frac { y - x } { 2 } } q ( s - t ) A ( s - t , s + t ) d t$ ; confidence 0.831

34. i130090217.png ; $( L ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \cong \text { varprojlim } A _ { n } ( k ^ { \prime } )$ ; confidence 0.661

35. j12002098.png ; $\leq 2 E [ X _ { 0 } ] + 2 E [ X _ { \infty } \operatorname { log } + \frac { X _ { \infty } } { E [ X _ { 0 } ] } ]$ ; confidence 0.541

36. j12002077.png ; $X = M ^ { 1 } - \operatorname { lim } _ { N \rightarrow \infty } \sum _ { n = - N } ^ { n = N } c _ { n } A ^ { n }$ ; confidence 0.947

37. j120020184.png ; $U _ { t } ^ { 1 } U _ { t } ^ { 2 } - \int _ { 0 } ^ { t } \nabla u _ { 1 } ( B _ { s } ) \cdot \nabla u _ { 2 } ( B _ { s } ) d s$ ; confidence 0.735

38. k05507010.png ; $H ^ { 2 r } ( M , C ) \neq 0 \quad \text { if } r = 1 , \dots , \frac { 1 } { 2 } \operatorname { dim } _ { C } M$ ; confidence 0.432

39. l12001050.png ; $\left\{ \begin{array} { c } { m } \\ { \lceil \frac { m + 1 } { 2 } \rceil } \end{array} \right\}$ ; confidence 0.282

40. l13008018.png ; $- \mathfrak { c } _ { 1 } + \mathfrak { c } _ { 3 } d ^ { \nu } \operatorname { log } ( \rho / | \omega | )$ ; confidence 0.515

41. l120170293.png ; $0 \rightarrow P _ { n } \rightarrow \ldots \rightarrow P _ { 0 } \rightarrow Z \rightarrow 0$ ; confidence 0.777

42. l12017044.png ; $\langle \alpha , b | \alpha = [ \alpha ^ { p } , b ^ { \gamma } ] , b = [ \alpha ^ { r } , b ^ { s } ] \rangle$ ; confidence 0.320

43. m13002030.png ; $\phi = ( \frac { 1 } { \operatorname { tanh } r } - \frac { 1 } { r } ) \frac { x _ { i } } { r } \sigma _ { i }$ ; confidence 0.982

44. n12010048.png ; $\sum _ { i = 0 } ^ { k } \alpha _ { i } y _ { m + i } = h \sum _ { i = 0 } ^ { k } \beta _ { i } f ( x _ { m } + i , y _ { m + i } )$ ; confidence 0.143

45. o13001080.png ; $A ( \alpha ^ { \prime } , \alpha , k ) \equiv - \frac { C } { 4 \pi } , \text { if } \Gamma u = u , k a \ll 1$ ; confidence 0.857

46. p13007081.png ; $= \operatorname { sup } \{ \int _ { K } M ( u ) d V : u \in \operatorname { PSH } ( \Omega ) , 0 < u < 1 \}$ ; confidence 0.932

47. p13007046.png ; $f ( z _ { 1 } , z _ { 2 } ) = ( | z _ { 1 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 } = ( | z _ { 2 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 }$ ; confidence 0.998

48. p13014052.png ; $D ( x _ { 0 } ) : = \operatorname { lim } _ { t \rightarrow + 0 } [ f ( x _ { 0 } + t n _ { 0 } ) - f ( x - t n _ { 0 } ) ]$ ; confidence 0.848

49. q12003045.png ; $\psi = ( \text { id } \otimes \varphi ) \circ L : A \rightarrow \operatorname { Fun } _ { q } ( G )$ ; confidence 0.524

50. s120040106.png ; $\operatorname { ch } ( \chi ) = \frac { 1 } { n ! } \sum _ { | \mu | = n } k _ { \mu } \chi _ { \mu } p _ { \mu }$ ; confidence 0.928

51. s12020069.png ; $S ^ { \lambda } = \operatorname { span } \{ e _ { t } : t _ { a } \lambda \square \text { tableau } \}$ ; confidence 0.051

52. s13051052.png ; $N _ { n } = \{ u \in V : n = \operatorname { min } m , F ( u ) \cap \cup _ { i < m } P _ { i } \neq \emptyset \}$ ; confidence 0.729

53. w12009096.png ; $\ldots \times \mathfrak { S } _ { \{ \lambda _ { 1 } + \ldots + \lambda _ { n - 1 } + 1 , \ldots , r \} }$ ; confidence 0.259

54. w130080164.png ; $Y ( \gamma ) = \psi ( z _ { 0 } , z _ { 0 } ) | _ { \gamma } = P \operatorname { exp } ( \oint _ { \gamma } A )$ ; confidence 0.794

55. z130110132.png ; $\frac { \mu _ { N } ( x ) } { M } \stackrel { P } { \rightarrow } \int _ { 0 } ^ { 1 } u ( 1 - u ) ^ { x - 1 } F ( d x )$ ; confidence 0.567

56. a130050212.png ; $\sum _ { n \leq x } \alpha ( n ) = A _ { 1 } x + O ( \sqrt { x } ) \quad \text { as } x \rightarrow \infty$ ; confidence 0.331

57. a12007082.png ; $A ( 0 ) u _ { 0 } + f ( 0 ) - \frac { d } { d t } A ( t ) ^ { - 1 } | _ { t = 0 } A ( 0 ) u _ { 0 } \in \overline { D ( A ( 0 ) ) }$ ; confidence 0.704

58. a12016046.png ; $A ( t _ { 0 } ) = A _ { 0 } , \dot { X } ( t ) = [ N ( X ( t ) , A ( t ) , t ) - X ( t ) ] \operatorname { exp } ( - k P ( t ) )$ ; confidence 0.365

59. a13012028.png ; $k = s \mu , v = s ^ { 2 } \mu , \lambda = \frac { s \mu - 1 } { \mu - 1 } , r = \frac { s ^ { 2 } \mu - 1 } { \mu - 1 }$ ; confidence 0.996

60. b12009016.png ; $\frac { \partial f ( z , t ) } { \partial t } = - f ( z , t ) \frac { 1 + k f ( z , t ) } { 1 - \dot { k } f ( z , t ) }$ ; confidence 0.781

61. b110220194.png ; $CH ^ { p } ( X ) ^ { 0 } = \operatorname { Ker } ( CH ^ { p } ( X ) \rightarrow H ^ { 2 p } B ( X _ { C } , Q ( p ) ) )$ ; confidence 0.124

62. b13019025.png ; $U ( f ; M _ { 1 } , M _ { 2 } ; H _ { 1 } , H _ { 2 } ) = \sum _ { h } \frac { S ( h f ^ { \prime } ; M _ { 1 } , M _ { 2 } ) } { h }$ ; confidence 0.777

63. b13023041.png ; $\operatorname { rist } _ { G } ( n ) = \langle \operatorname { rist } _ { G } ( u ) : | u | = n \rangle$ ; confidence 0.469

64. c1300408.png ; $\beta ( z ) : = \frac { 1 } { 2 } [ \psi ( \frac { 1 } { 2 } z + \frac { 1 } { 2 } ) - \psi ( \frac { 1 } { 2 } z ) ] =$ ; confidence 0.999

65. c12008037.png ; $\Delta ( A _ { 1 } ) = \sum _ { i = 0 } ^ { m } ( I _ { m } \otimes D _ { m - i } ) A _ { 1 } ^ { i } = 0 ( D _ { 0 } = I _ { n } )$ ; confidence 0.459

66. c12008087.png ; $\left. \begin{array} { l l } { E _ { 1 } } & { E _ { 2 } } \\ { E _ { 3 } } & { E _ { 4 } } \end{array} \right.$ ; confidence 0.730

67. c120180492.png ; $\mathfrak { g } = t ^ { 2 } \sum _ { i , j } \mathfrak { g } _ { i j } ( x , t ) d x ^ { i } \bigotimes d x ^ { j } +$ ; confidence 0.413

68. c120210127.png ; $\int _ { A } \operatorname { exp } ( h ^ { \prime } \Delta _ { N } ^ { * } ( \theta ) ) d P _ { n , \theta }$ ; confidence 0.635

69. c12027015.png ; $\omega = \operatorname { inf } _ { p \in \Omega } \frac { Vol ( \Omega _ { p } ) } { \alpha ( n - 1 ) }$ ; confidence 0.663

70. c12030028.png ; $( H ^ { \otimes r } , H ^ { \otimes r + k } ) \rightarrow ( H ^ { \otimes r + 1 } , H ^ { \otimes r + 1 + k } )$ ; confidence 0.600

71. d12011032.png ; $\operatorname { lim } _ { i \rightarrow \infty } x _ { i _ { i } } n _ { j } = 0 \text { for all } j \in N$ ; confidence 0.311

72. d120230107.png ; $C _ { l } = ( \frac { u _ { i } v _ { j } ^ { * } } { f _ { i } - a _ { j } ^ { * } } ) , u _ { i } , v _ { i } \in C ^ { 1 \times r }$ ; confidence 0.648

73. e13004036.png ; $= ( \Omega _ { + } - 1 ) ( g - \mathfrak { g } ) \psi ( t ) + ( \Omega _ { + } - 1 ) g \mathfrak { v } \psi ( t )$ ; confidence 0.087

74. e120230175.png ; $\sigma ^ { 2 k ^ { * } } [ E ( L ) ( Z ^ { 2 k } ) ] = \sigma ^ { k + 1 ^ { * } } [ \Omega ( d L \Delta ) ( Z ^ { k + 1 } ) ]$ ; confidence 0.758

75. f13016044.png ; $\leq \operatorname { max } \{ \mu ( M , P ) + Kdim ( R / P ) : P \in j - \operatorname { Spec } ( R ) \}$ ; confidence 0.315

76. f12014014.png ; $\frac { 1 } { \lambda } = \operatorname { sup } \frac { | D ( h ) - D ^ { * } ( h ) | } { D ( h ) + D ^ { * } ( h ) }$ ; confidence 0.998

77. g130030109.png ; $\tau _ { \varepsilon } ( x ) = \frac { \varepsilon } { \pi } ( x ^ { 2 } + \varepsilon ^ { 2 } ) ^ { - 1 }$ ; confidence 0.795

78. g130060120.png ; $: = \{ B = [ b _ { i } , j ] : b _ { i , i } = a _ { i , i } , \text { and } r _ { i } ( B ) = r _ { i } ( A ) , 1 \leq i \leq n \}$ ; confidence 0.207

79. h13005041.png ; $\frac { d ^ { 2 } \psi } { d x ^ { 2 } } + [ \lambda \rho ( x , t ) - u ( x , t ) ] \psi = 0 , - \infty < x < \infty$ ; confidence 0.993

80. i130090224.png ; $Y = \operatorname { Gal } ( M ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \otimes Z _ { p } [ \chi ]$ ; confidence 0.898

81. i130090223.png ; $X = \operatorname { Gal } ( L ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \otimes Z _ { p } [ \chi ]$ ; confidence 0.772

82. l12010023.png ; $\approx ( 2 \pi ) ^ { - n } \int _ { R ^ { n } \times R ^ { n } } [ p ^ { 2 } + V ( x ) ] _ { - } ^ { \gamma } d p d x =$ ; confidence 0.680

83. l13010033.png ; $f _ { s l } ( x ) : = - \frac { 1 } { 4 \pi } \int _ { S ^ { 1 } } \hat { f } _ { p p } ( \alpha , \alpha x ) d \alpha$ ; confidence 0.254

84. m12007062.png ; $m ( P ) > c _ { 1 } ( \operatorname { log } \operatorname { log } d / \operatorname { log } d ) ^ { 3 }$ ; confidence 0.987

85. m13011037.png ; $\frac { \partial \phi } { \partial t } = ( \frac { \partial \phi ( x , t ) } { \partial t } ) | _ { x }$ ; confidence 0.960

86. m12015065.png ; $\frac { 1 } { \beta _ { p } ( \alpha , b ) } | U | ^ { \alpha - ( p + 1 ) / 2 } | I _ { p } - U | ^ { \phi - ( p + 1 ) / 2 }$ ; confidence 0.250

87. n067520310.png ; $A = \sum _ { m , n \geq 0 } \int K _ { q , m } ( x _ { 1 } , \ldots , x _ { n } ; y _ { 1 } , \ldots , y _ { m } ) \times$ ; confidence 0.178

88. o13001020.png ; $v ( x , \alpha , k ) = \frac { e ^ { i k r } } { r } A ( \alpha ^ { \prime } , \alpha , k ) + o ( \frac { 1 } { r } )$ ; confidence 0.871

89. o0681706.png ; $E e ^ { i t \omega ^ { 2 } } = \prod _ { k = 1 } ^ { \infty } ( 1 - \frac { 2 i t } { \pi ^ { 2 } k ^ { 2 } } ) ^ { - 1 / 2 }$ ; confidence 0.848

90. p12017013.png ; $\operatorname { ker } \delta _ { A , B } \subseteq \operatorname { ker } \delta _ { A , B } ^ { * }$ ; confidence 0.231

91. r13007068.png ; $( f , g ) : = ( \sum _ { j = 1 } ^ { J } K ( x , y _ { j } ) c _ { j } , \sum _ { m = 1 } ^ { M } K ( x , z _ { m } ) \beta _ { m } ) =$ ; confidence 0.871

92. s13011026.png ; $\partial _ { n } \ldots \partial _ { 1 } \mathfrak { S } _ { w _ { n + 1 } } = \mathfrak { S } _ { w _ { n } }$ ; confidence 0.260

93. s1301104.png ; $H ^ { * } ( F _ { n } , Z ) \simeq Z [ x _ { 1 } , \dots , x _ { n } ] / Z ^ { + } [ x _ { 1 } , \dots , x _ { n } ] ^ { S _ { n } }$ ; confidence 0.353

94. s1200507.png ; $S _ { n + 1 } ( z ) = \frac { 1 } { z } \frac { S _ { n } ( z ) - S _ { n } ( 0 ) } { 1 - S _ { n } ( 0 ) S _ { n } ( z ) } , n \geq 0$ ; confidence 0.660

95. s13041041.png ; $\sum _ { j = n - k } ^ { n + 1 } b _ { n , j } P _ { j } ( x ) = \sum _ { j = n - k } ^ { n + 1 } \beta _ { n + 1 , j } Q _ { j } ( x )$ ; confidence 0.708

96. s13064036.png ; $G ( \alpha ) = \operatorname { exp } ( [ \operatorname { log } \operatorname { det } a ] _ { 0 } )$ ; confidence 0.685

97. v12002035.png ; $f ^ { * } : \overline { H } \square ^ { * } ( Y , G ) \rightarrow \overline { H } \square ^ { * } ( X , G )$ ; confidence 0.481

98. v120020133.png ; $\Lambda ( F ) = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \operatorname { tr } ( r * n \circ t * n ^ { - 1 } )$ ; confidence 0.358

99. v12002043.png ; $f ^ { * } : \overline { H } \square ^ { q } ( Y , G ) \rightarrow \overline { H } \square ^ { q } ( X , G )$ ; confidence 0.481

100. w120090259.png ; $\mathfrak { B } = \{ e _ { \pm } \alpha , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}$ ; confidence 0.381

101. w12011021.png ; $= | t | ^ { - n } \int \int e ^ { - 2 i \pi t ^ { - 1 } y \cdot \eta } _ { \alpha ( x + y , \xi + \eta ) d y d \eta }$ ; confidence 0.344

102. w13008060.png ; $\frac { \Omega _ { x } } { \partial T _ { m } } = \frac { \partial \Omega _ { m } } { \partial T _ { N } }$ ; confidence 0.071

103. z13001057.png ; $= \frac { - 4 z } { z + 2 } + \frac { 4 z } { ( z + 2 ) ^ { 2 } } - \frac { 3 z } { ( z + 2 ) ^ { 3 } } + \frac { 4 z } { z + 3 }$ ; confidence 0.999

104. z130110144.png ; $\mu _ { N } \rightarrow \infty \quad \text { but } \frac { \mu _ { \aleph } } { n } \rightarrow 0$ ; confidence 0.229

105. a130040337.png ; $\operatorname { tg } E ( \lambda x _ { 0 } , \ldots , x _ { x } - 1 , \lambda y 0 , \ldots , y _ { n } - 1 )$ ; confidence 0.167

106. a130050224.png ; $\sum _ { n \leq x } G ( n ) = A _ { G } x ^ { \delta } + O ( x ^ { \eta } ) \text { as } x \rightarrow \infty$ ; confidence 0.597

107. a12011017.png ; $A ( i , 0 ) = A ( i - 1,1 ) \text { for } i \geq 1 , A ( i , n ) = A ( i - 1 , A ( i , n - 1 ) ) \text { for } i \geq 1 , n$ ; confidence 0.921

108. a11032011.png ; $+ h \sum _ { j = 1 } ^ { s } B _ { j } ( h T ) [ f ( t _ { m } + c _ { j } h , u _ { m + 1 } ^ { ( j ) } ) - T u _ { m j } ^ { ( j ) } + 1 ]$ ; confidence 0.083

109. a12018056.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { S _ { n + 1 } - S } { S _ { n } - S } = \lambda$ ; confidence 0.571

110. a130180125.png ; $\exists b _ { i } : b = \{ b _ { 0 } , \dots , b _ { i } - 1 , b _ { i } , b _ { i } + 1 , \dots , b _ { p } - 1 \} \in R \}$ ; confidence 0.084

111. a13029045.png ; $HF _ { * } ^ { \text { inst } } ( Y , P _ { Y } ) \cong HF _ { * } ^ { \text { symp } } ( M ( P ) , L _ { 0 } , L _ { 1 } )$ ; confidence 0.183

112. b12010039.png ; $= F _ { N } ( X _ { 1 } ( - t , x _ { 1 } , \ldots , x _ { N } ) , \ldots , X _ { N } ( - t , x _ { 1 } , \ldots , x _ { N } ) )$ ; confidence 0.275

113. b11066032.png ; $H f ( x ) = \operatorname { lim } _ { \epsilon } \lfloor 0 \int _ { | t | > \epsilon } f ( x - t ) / t d t$ ; confidence 0.520

114. b120430173.png ; $\Delta f = 1 \bigotimes f + x \bigotimes \partial _ { q , x } f + y \otimes \partial _ { q , y } f +$ ; confidence 0.239

115. c120010162.png ; $f ( z ) = \sum _ { k = 1 } ^ { \infty } \frac { c _ { k } } { ( 1 + \langle z , \alpha _ { k } \rangle ) ^ { n } }$ ; confidence 0.698

116. d12023096.png ; $P = ( \frac { u _ { i } u _ { j } ^ { * } - v _ { i } v _ { j } ^ { * } } { 1 - f _ { i } f _ { j } ^ { * } } ) _ { i , j = 0 } ^ { n - 1 }$ ; confidence 0.936

117. e13003056.png ; $\operatorname { Eis } ( \omega ) = \sum _ { \gamma \in \Gamma / \Gamma _ { P } } \gamma \omega$ ; confidence 0.810

118. e120230143.png ; $A ( \sigma ) = \int _ { M } L \circ \sigma ^ { k } \Delta = \int _ { M } \sigma ^ { k ^ { * } } ( L \Delta )$ ; confidence 0.612

119. f1200407.png ; $f ^ { c ( \varphi ) } ( w ) = \operatorname { sup } _ { x \in X } \{ \varphi ( x , w ) - f ( x ) \} ( w \in W )$ ; confidence 0.324

120. f1202304.png ; $[ . , ] : \Omega ^ { k } ( M ; T M ) \times \Omega ^ { l } ( M ; T M ) \rightarrow \Omega ^ { k + l } ( M ; T M )$ ; confidence 0.407

121. g12001013.png ; $\int _ { - \infty } ^ { \infty } ( G _ { b } ^ { \alpha } f ) ( \omega ) d \dot { b } = \hat { f } ( \omega )$ ; confidence 0.739

122. g120040173.png ; $\sum _ { \alpha \in Z ^ { n } } \frac { \alpha _ { \alpha } } { ( | \alpha | ! ) ^ { s - 1 } } x ^ { \alpha }$ ; confidence 0.157

123. h120120159.png ; $T ( \nabla ) _ { \infty } : ( T ( H ( Y ) ) , \partial _ { \infty } ) \rightarrow \overline { B } ( Y )$ ; confidence 0.991

124. i12001020.png ; $\operatorname { sup } _ { x \neq y \in \Omega } | u ( x ) - u ( y ) | ( \sigma | x - y | ) ^ { - 1 } < \infty$ ; confidence 0.972

125. i12008079.png ; $Z = \sum _ { S _ { 1 } = \pm 1 } | s _ { 1 } | P ^ { N } | S _ { 1 } \rangle = \lambda _ { + } ^ { N } + \lambda ^ { N }$ ; confidence 0.081

126. j12002096.png ; $E [ X _ { 0 } ] + E [ X _ { \infty } \operatorname { log } + \frac { X _ { \infty } } { E [ X _ { 0 } ] } ] \leq$ ; confidence 0.435

127. j120020204.png ; $\int _ { I } | \varphi - \varphi _ { I } | ^ { 2 } \frac { d \vartheta } { 2 \pi } \leq c _ { 1 } ^ { 2 } | I |$ ; confidence 0.284

128. k12008046.png ; $S _ { r } = \{ ( v _ { 0 } , \dots , v _ { r } ) \in R ^ { r + 1 } : v _ { j } \geq 0 , \sum _ { j = 0 } ^ { r } v _ { j } = 1 \}$ ; confidence 0.419

129. l12004075.png ; $\hat { a } _ { i } ^ { + } = u _ { i } ^ { n } + \frac { \Delta t } { \Delta x } ( f _ { i } ^ { n } - f _ { i + 1 } ^ { n } )$ ; confidence 0.323

130. l13001060.png ; $C _ { 1 } \operatorname { ln } ^ { n } N \leq \| S _ { N B } \| \leq C _ { 2 } \operatorname { ln } ^ { n } N$ ; confidence 0.826

131. l12006079.png ; $\langle \lambda | f ( z ) ) = \frac { 1 } { \lambda - z } \langle \lambda | V \phi ) ( \phi , f ( z ) )$ ; confidence 0.836

132. m12016023.png ; $A X B + C \sim E _ { q , n } ( A M B + C , ( A \Sigma A ^ { \prime } ) \otimes ( B ^ { \prime } \Phi B ) , \psi )$ ; confidence 0.628

133. m1202409.png ; $\psi [ 1 ] = \psi - \frac { \varphi \Omega ( \varphi , \psi ) } { \Omega ( \varphi , \varphi ) }$ ; confidence 0.985

134. o12005082.png ; $\operatorname { sup } _ { \lambda > 0 } \varphi ^ { \prime } ( a u ) / \varphi ^ { \prime } ( u ) < 1$ ; confidence 0.083

135. s12004074.png ; $s _ { \lambda } = \frac { 1 } { n ! } \sum _ { | \mu | = n } k _ { \mu } \chi _ { \mu } ^ { \lambda } p _ { \mu }$ ; confidence 0.708

136. s130510150.png ; $D = \{ u \in V : \sigma ( u ) = \infty ( K ) , 0 \notin K \} , N = \{ u \in V : 0 < \sigma ( u ) < \infty \} U$ ; confidence 0.790

137. s13062016.png ; $( \operatorname { cos } \alpha ) y ( 0 ) + ( \operatorname { sin } \alpha ) y ^ { \prime } ( 0 ) = 0$ ; confidence 0.820

138. s130620162.png ; $y ( x , \lambda ) = \frac { \operatorname { sin } x } { 1 + ( 2 x - \operatorname { sin } 2 x ) ^ { 2 } }$ ; confidence 0.997

139. s12032016.png ; $[ x , y ] = - ( - 1 ) ^ { p ( x ) p ( y ) } [ y , x ] , [ x , [ y , z ] ] = [ [ x , y ] , z ] + ( - 1 ) ^ { p ( x ) p ( y ) } [ y , [ x , z ] ]$ ; confidence 0.989

140. s13065054.png ; $S _ { k + 1 } ( z ) = z ^ { - 1 } \frac { S _ { k } ( z ) - S _ { k } ( 0 ) } { 1 - \overline { S } _ { k } ( 0 ) S _ { k } ( z ) }$ ; confidence 0.545

141. t12006011.png ; $= \frac { 3 } { 5 } \gamma \int _ { R ^ { 3 } } \rho ( x ) ^ { 5 / 3 } d x - \int _ { R ^ { 3 } } V ( x ) \rho ( x ) d x +$ ; confidence 0.644

142. t12013030.png ; $= \oint _ { z = \infty } \tau _ { n + 1 } ( x , y - [ z ] ) \tau _ { m } ( x ^ { \prime } , y ^ { \prime } + [ z ] ) x$ ; confidence 0.883

143. t12020063.png ; $R _ { n } = \operatorname { min } _ { z _ { j } } \operatorname { max } _ { k = 1 , \ldots , n } | s _ { k } |$ ; confidence 0.225

144. w13004038.png ; $N = \frac { 1 } { | g | ^ { 2 } + 1 } ( 2 \operatorname { Re } g , 2 \operatorname { Im } g , | g | ^ { 2 } - 1 )$ ; confidence 0.511

145. w120110221.png ; $\operatorname { sup } _ { X \in \Phi } \| \alpha ^ { ( k ) } ( X ) \| _ { G _ { X } } m ( X ) ^ { - 1 } < \infty$ ; confidence 0.564

146. w12011059.png ; $A ( u , v ) ( \xi , x ) = \int u ( z - \frac { x } { 2 } ) \nabla ( z + \frac { x } { 2 } ) e ^ { - 2 i \pi z . \xi } d z$ ; confidence 0.810

147. w13009058.png ; $\| \varphi \| _ { L ^ { 2 } ( \mu ) } ^ { 2 } = \sum _ { n = 0 } ^ { \infty } n ! | f _ { n } | _ { H } ^ { 2 } \otimes$ ; confidence 0.404

148. z13001045.png ; $K _ { i } = \operatorname { lim } _ { z \rightarrow z _ { i } } [ ( z - z _ { i } ) \frac { h ( z ) } { g ( z ) } ]$ ; confidence 0.946

149. z13003066.png ; $\hat { f } ( - 2 \pi w ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i w t } ( Z f ) ( t , w ) d t$ ; confidence 0.757

150. z13011033.png ; $G _ { n } ( f ( k , n ) ) = \operatorname { max } \{ k ^ { \prime } : f _ { ( k ^ { \prime } , n ) } = f ( k , n ) \}$ ; confidence 0.516

151. a130040541.png ; $h ( \psi ^ { i } ) \in C ( \{ h ( \varphi _ { 0 } ^ { i } ) , \ldots , h ( \varphi _ { n _ { i } - 1 } ^ { i } ) \} )$ ; confidence 0.325

152. a12005053.png ; $| \frac { \partial } { \partial t } U ( t , s ) \| \leq \frac { C } { t - s } , \quad 0 \leq s < t \leq T$ ; confidence 0.766

153. a13008045.png ; $\alpha ( s ) = \frac { f ( L ( s ) ) } { g ( L ( s ) ; m ( s ) , s ) } = \frac { f ( R ( s ) ) } { g ( R ( s ) ; m ( s ) , s ) }$ ; confidence 0.999

154. a13018018.png ; $L ( \tau ) = \langle Fm _ { \tau } , Mod _ { \tau } , F _ { \tau } , mng _ { \tau } , t _ { \tau } \rangle$ ; confidence 0.140

155. a13020013.png ; $\langle x y z \rangle - \langle z y x \rangle = \langle z x y \rangle - \langle x z y \rangle$ ; confidence 0.728

156. b13012080.png ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } \| f V _ { \varepsilon } \| _ { A } * = 0$ ; confidence 0.931

157. b13025014.png ; $\angle \Omega ^ { \prime } B A = \angle \Omega ^ { \prime } C B = \angle \Omega ^ { \prime } A C$ ; confidence 0.997

158. b13029058.png ; $( \alpha _ { 1 } , \dots , a _ { i - 1 } ) : \alpha _ { i } = ( \alpha _ { 1 } , \dots , \alpha _ { i - 1 } ) : m$ ; confidence 0.141

159. c13005040.png ; $\operatorname { Aut } ( G , S ) = \{ \sigma \in \operatorname { Aut } ( G ) : S ^ { \sigma } = S \}$ ; confidence 0.331

160. c13007026.png ; $\left( \begin{array} { c } { m + 2 } \\ { 2 } \end{array} \right) = \frac { ( m + 2 ) ( m + 1 ) } { 2 }$ ; confidence 0.990

161. c120180180.png ; $g ^ { - 1 } \{ p , q , r , s \} = g ^ { - 1 } \{ p , q \} g ^ { - 1 } \{ r , s \} = g ^ { - 1 } \{ r , s \} g ^ { - 1 } \{ p , q \}$ ; confidence 0.996

162. c12031054.png ; $e _ { \lambda } ^ { ran } ( F _ { d } ) = \operatorname { inf } _ { Q _ { n } } e ^ { ran } ( Q _ { n } , F _ { d } )$ ; confidence 0.160

163. d12002046.png ; $= \operatorname { min } _ { k \in P } c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } )$ ; confidence 0.488

164. d12011033.png ; $\operatorname { lim } _ { i \rightarrow \infty } \sum _ { j = 1 } ^ { \infty } x _ { i j } x _ { j } = 0$ ; confidence 0.142

165. d12016060.png ; $\| f \| \neq \operatorname { dist } ( f , C ( S ) \otimes \pi _ { k } ( T ) + \pi ( S ) \otimes C ( T ) )$ ; confidence 0.736

166. e12016046.png ; $\partial _ { r } ( r J ^ { - 1 } \partial _ { r } J ) + \partial _ { z } ( r J ^ { - 1 } \partial _ { z } J ) = 0$ ; confidence 0.648

167. e12026012.png ; $L _ { \mu } ( \theta ) = \int _ { E } \operatorname { exp } \langle \theta , x \rangle \mu ( d x )$ ; confidence 0.740

168. f120110200.png ; $C _ { \delta } = \{ z : | \operatorname { Im } z | < \delta ( | \operatorname { Re } _ { z | } + 1 ) \}$ ; confidence 0.519

169. f12021069.png ; $= \frac { ( n _ { 1 } + l ) ! } { ! ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { 2 } } + \ldots$ ; confidence 0.665

170. f12023033.png ; $D ( \varphi \wedge \psi ) = D ( \varphi ) \wedge \psi + ( - 1 ) ^ { k l } \varphi \wedge D ( \psi )$ ; confidence 0.995

171. g13004046.png ; $\operatorname { limsup } _ { r \rightarrow 0 } \frac { H ^ { m } ( E \cap B ( x , r ) ) } { r ^ { m } } > 0$ ; confidence 0.556

172. h12002085.png ; $s _ { j } ( T ) = \operatorname { inf } \{ \| T - R \| : \operatorname { rank } R \leq j \} , j \geq 0$ ; confidence 0.936

173. i13002022.png ; $S _ { k } = \left( \begin{array} { c } { n } \\ { k } \end{array} \right) \frac { ( n - k ) ! } { n ! }$ ; confidence 0.636

174. i130090145.png ; $\lambda _ { p } ( k _ { \infty } / k ) = \mu _ { p } ( k _ { \infty } / k ) = \nu _ { p } ( k _ { \infty } / k ) = 0$ ; confidence 0.839

175. j120020216.png ; $\alpha \leq \frac { 1 } { | l _ { j } | } \int _ { I _ { j } } | u ( \vartheta ) | d \vartheta < 2 \alpha$ ; confidence 0.721

176. j13007066.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z ) = \eta \in \partial \Delta$ ; confidence 0.934

177. k1300107.png ; $\langle L _ { + } \rangle = A \langle L _ { 0 } \rangle + A ^ { - 1 } \langle L _ { \infty } \rangle$ ; confidence 0.405

178. k13001035.png ; $f ( \vec { D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \vec { D } ) } \langle D \rangle$ ; confidence 0.497

179. l12010050.png ; $| e _ { 1 } | ^ { \gamma } \leq L _ { \gamma , n } ^ { 1 } \int _ { R ^ { n } } V _ { - } ( x ) ^ { \gamma + n / 2 } d x$ ; confidence 0.311

180. m12003039.png ; $V ( T , F _ { \theta } ) = \int \operatorname { IF } ( x ; T , F _ { \theta } ) ^ { 2 } d F _ { \theta } ( x )$ ; confidence 0.919

181. m13011062.png ; $v _ { i } = - \frac { D _ { x _ { i } } } { D t } = ( \frac { \partial x _ { i } } { \partial t } ) | _ { x _ { k } 0 }$ ; confidence 0.154

182. m130140147.png ; $d \zeta / \zeta = d \zeta _ { 2 } / \zeta _ { 2 } \wedge \ldots \wedge d \zeta _ { n } / \zeta _ { n }$ ; confidence 0.740

183. m13018020.png ; $g ( x ) = \sum _ { y : y \geq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \geq x } \mu ( x , y ) g ( y )$ ; confidence 0.747

184. m13018019.png ; $g ( x ) = \sum _ { y : y \leq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \leq x } g ( y ) \mu ( y , x )$ ; confidence 0.855

185. o130010132.png ; $\operatorname { sup } _ { \alpha ^ { \prime } , \alpha \in S ^ { 2 } } | A _ { 1 } - A _ { 2 } | < \delta$ ; confidence 0.959

186. p13007024.png ; $M f = \operatorname { det } ( \frac { \partial ^ { 2 } f } { \partial z _ { i } \partial z _ { j } } )$ ; confidence 0.974

187. r13007047.png ; $= c \sum _ { j = 1 } ^ { \infty } ( A \varphi _ { j } , \varphi _ { j } ) _ { 0 } = c \Lambda ^ { 2 } < \infty$ ; confidence 0.984

188. r130070104.png ; $\| f \| _ { 1 } ^ { 2 } = \operatorname { lim } _ { n \rightarrow \infty } \| f _ { n } \| _ { 1 } ^ { 2 } =$ ; confidence 0.590

189. r13008051.png ; $K _ { D } ( z , \zeta ) = \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( z ) \overline { \phi _ { j } ( \zeta ) }$ ; confidence 0.978

190. s0860209.png ; $| \phi ( t _ { 1 } ) - \phi ( t _ { 2 } ) | \leq C | t _ { 1 } - t _ { 2 } | ^ { \alpha } , \quad 0 < \alpha \leq 1$ ; confidence 0.970

191. s13059042.png ; $F _ { R } = \frac { H _ { X } ^ { ( - n ) } H _ { n } ^ { ( - n + 3 ) } } { H _ { n } ^ { ( - n + 2 ) } H _ { n - 1 } ^ { ( - n + 1 ) } }$ ; confidence 0.057

192. w13007010.png ; $\operatorname { ch } V = \sum _ { \mu \in h ^ { * } } ( \operatorname { dim } V _ { \mu } ) e ^ { \mu }$ ; confidence 0.357

193. w13009078.png ; $\{ \varphi _ { n _ { 1 } , n _ { 2 } , \ldots } : n _ { j } \geq 0 , n _ { 1 } + n _ { 2 } + \ldots = n , n \geq 0 \}$ ; confidence 0.183

194. y1200405.png ; $\operatorname { lim } _ { j \rightarrow \infty } \int _ { \Omega } \varphi ( x , f j ( x ) ) d x =$ ; confidence 0.690

195. z13003067.png ; $f ( 2 \pi t ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i x t } ( Z \hat { f } ) ( x , t ) d x$ ; confidence 0.805

196. a12005087.png ; $| \prod _ { j = 1 } ^ { k } ( \lambda - A ( t _ { j } ) ) ^ { - 1 } \| _ { X } \leq M ( \lambda - \beta ) ^ { - k }$ ; confidence 0.936

197. a12006028.png ; $D ( A ) = \{ u \in [ H ^ { 1 } ( \Omega ] ^ { p } : u ( x ) \in P ( x ) \text { a.e. on } \partial \Omega \}$ ; confidence 0.643

198. a130060117.png ; $G ^ { \# } ( n ) \sim C Z _ { G } ( q ^ { - 1 } ) q ^ { n } n ^ { - \alpha } \text { asn } \rightarrow \infty$ ; confidence 0.776

199. a11032023.png ; $B _ { j } ( z ) = \sum _ { l = 0 } ^ { \rho _ { s + 1 } } R _ { l + 1 } ^ { ( s + 1 ) } ( z ) \lambda _ { l j } ^ { ( s + 1 ) }$ ; confidence 0.113

200. b11002024.png ; $\operatorname { sup } _ { \alpha \in U } | b ( u , v ) | > 0 , \forall v \in V \backslash \{ 0 \} )$ ; confidence 0.321

201. b12034018.png ; $\frac { 1 } { 3 \sqrt { n } } < K _ { n } < \frac { 2 \sqrt { \operatorname { log } n } } { \sqrt { n } }$ ; confidence 0.996

202. b13020086.png ; $\mathfrak { g } _ { \pm } = \oplus _ { \alpha \in \Delta _ { \pm } } \mathfrak { g } ^ { \alpha }$ ; confidence 0.871

203. b13026030.png ; $\sum _ { x \in f ^ { - 1 } ( y ) } \operatorname { sign } \operatorname { det } f ^ { \prime } ( x )$ ; confidence 0.975

204. c130160156.png ; $NC = \text { ASPACETIME } [ \operatorname { log } n , ( \operatorname { log } n ) ^ { O ( 1 ) } ]$ ; confidence 0.357

205. c130160189.png ; $L \subseteq NL \subseteq NC \subseteq P \subseteq NP \subseteq PH \subseteq PSPACE$ ; confidence 0.906

206. c120210114.png ; $\Lambda _ { n } ( \theta ) = \operatorname { log } ( d P _ { n , \theta _ { n } } / P _ { n , \theta } )$ ; confidence 0.827

207. d120020229.png ; $\overline { x } = \sum _ { k \in R ^ { \prime } } \overline { \mu } _ { k } \overline { x } ^ { ( k ) }$ ; confidence 0.152

208. d1203109.png ; $f ( T ) = \frac { 1 } { 2 \pi i } \int _ { \partial U } f ( \lambda ) ( \lambda - T ) ^ { - 1 } d \lambda$ ; confidence 0.982

209. e12010035.png ; $f ^ { em } = 0 = \operatorname { div } t ^ { em } f - \frac { \partial G ^ { em f } } { \partial t }$ ; confidence 0.071

210. e12023034.png ; $A ( \sigma ) = \int _ { M } L ( \sigma ^ { 1 } ( x ) ) d x = \int _ { M } L ( x , y ( x ) , y ^ { \prime } ( x ) ) d x$ ; confidence 0.319

211. f120110218.png ; $O ( e ^ { - \varepsilon | \operatorname { Re } \cdot Z | - H _ { L } } ( \operatorname { Re } z ) )$ ; confidence 0.118

212. g1200105.png ; $g _ { \alpha } ( t ) = \frac { 1 } { 2 \sqrt { \pi \alpha } } e ^ { - t ^ { 2 } / ( 4 \alpha ) } , \alpha > 0$ ; confidence 0.919

213. g13006043.png ; $( \lambda - \alpha _ { j } , i ) x _ { i } = \sum _ { j = 1 \atop j \neq i } ^ { n } \alpha _ { i , j } x _ { j }$ ; confidence 0.086

214. i13006088.png ; $g ( t ) : = - \frac { 2 } { \pi } \int _ { 0 } ^ { \infty } \delta ( k ) \operatorname { sin } ( k t ) d k$ ; confidence 0.791

215. i0530309.png ; $d f ( t , X _ { t } ) = [ f _ { t } ^ { \prime } ( t , X _ { t } ) + \alpha ( t ) f _ { X } ^ { \prime } ( t , X _ { t } ) +$ ; confidence 0.983

216. j13003030.png ; $[ \alpha \square b ^ { * } , x \square y ^ { * } ] = \{ a b x \} \square y ^ { * } - x \square \{ y a b \}$ ; confidence 0.748

217. j1200109.png ; $\operatorname { deg } F = \operatorname { max } _ { i } \operatorname { deg } F _ { i } \leq 2$ ; confidence 0.934

218. j13004066.png ; $P _ { \varphi } ( D _ { 1 } * D _ { 2 } ) ( v ) = P _ { \varphi } ( D _ { 1 } ) ( v ) P _ { \varphi } ( D _ { 2 } ) ( v )$ ; confidence 0.491

219. j130040115.png ; $\frac { P _ { 2 } ( v , z ) - \frac { v ^ { - 1 } - v } { z } } { z ( ( \frac { v ^ { - 1 } - v } { z } ) ^ { 2 } - 1 ) } = - v$ ; confidence 0.463

220. k12008067.png ; $\kappa _ { p } ( f ) = K _ { p } ( \operatorname { Re } ( f ) ) + i K _ { p } ( \operatorname { Im } ( f ) )$ ; confidence 0.943

221. k12010055.png ; $\bigwedge _ { j = 1 } ^ { m } \frac { d z _ { j } - d z _ { j } ^ { \prime } } { z _ { j } - z _ { j } ^ { \prime } }$ ; confidence 0.632

222. k12012025.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x = \infty$ ; confidence 0.999

223. k12012024.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x < \infty$ ; confidence 0.999

224. k055840335.png ; $L ( \lambda ) = \lambda ^ { n } I + \lambda ^ { n - 1 } B _ { n - 1 } + \ldots + \lambda B _ { 1 } + B _ { 0 }$ ; confidence 0.904

225. l1200409.png ; $u _ { i } ^ { n + 1 } = u _ { i } ^ { n } + \frac { \Delta t ^ { n } } { \Delta x } [ f _ { i - 1 / 2 } - f _ { i + 1 / 2 } ]$ ; confidence 0.830

226. l12007016.png ; $\left( \begin{array} { c } { v _ { 1 } , t } \\ { \vdots } \\ { v _ { k , t } } \end{array} \right)$ ; confidence 0.522

227. m12023051.png ; $d f _ { t } ( x ) = 0 \Leftrightarrow \partial f ( x ) \ni 0 \Leftrightarrow f _ { t } ( x ) = f ( x )$ ; confidence 0.974

228. o13001042.png ; $f ( x ) = \frac { 1 } { ( 2 \pi ) ^ { 3 / 2 } } \int _ { R ^ { 3 } } \hat { f } ( \xi ) u ( x , \xi ) d \xi , \xi : = k$ ; confidence 0.238

229. o13002018.png ; $D = \operatorname { liminf } _ { x \rightarrow \infty } M ( r _ { 1 } , r _ { 2 } ) ^ { 1 / n } \geq 22$ ; confidence 0.322

230. q12005075.png ; $B _ { new } = B - \frac { B s s ^ { T } B } { s ^ { T } B s } + \frac { y y ^ { T } } { y ^ { T } s } + \theta . w w ^ { T }$ ; confidence 0.463

231. s13011045.png ; $\mathfrak { S } _ { \mathfrak { d } } = \mathfrak { x } _ { \mathfrak { l } } ^ { \mathfrak { W } }$ ; confidence 0.089

232. s13041035.png ; $T _ { N } ( x ) = \sum _ { j = n - k } ^ { n + 1 } \frac { b _ { n } , j } { j } P _ { j } ^ { \prime } ( x ) , n \geq k + 1$ ; confidence 0.181

233. s12032095.png ; $\operatorname { str } ( T ) = \operatorname { tr } P - ( - 1 ) ^ { p ( S ) } \operatorname { tr } S$ ; confidence 0.889

234. s13065045.png ; $F _ { \mu } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) d \mu ( \theta )$ ; confidence 0.237

235. s13065031.png ; $\operatorname { lim } _ { n \rightarrow \infty } \phi _ { n } ^ { * } ( z ) = D _ { \mu } ( z ) ^ { - 1 }$ ; confidence 0.757

236. s13065025.png ; $c _ { \mu } = \int _ { - \pi } ^ { \pi } \operatorname { log } \mu ^ { \prime } ( \theta ) d \theta$ ; confidence 0.954

237. v1301108.png ; $\frac { b } { h } = \frac { 1 } { \pi } \operatorname { cosh } ^ { - 1 } \sqrt { 2 } \approx 0.2806$ ; confidence 0.980

238. w12005039.png ; $D _ { n } ^ { * } = R [ x _ { 1 } , \ldots , x _ { n } ] / \langle x _ { 1 } , \ldots , x _ { n } \rangle ^ { r + 1 }$ ; confidence 0.143

239. w13008026.png ; $\sqrt { \lambda } d \lambda + \text { (holomorphic), as } \lambda \rightarrow \infty$ ; confidence 0.492

240. w13009099.png ; $I _ { n } ( g ) = \int _ { [ 0,1 ] ^ { n } } g ( t _ { 1 } , \ldots , t _ { n } ) d B ( t _ { 1 } ) \ldots d B ( t _ { n } )$ ; confidence 0.258

241. w12019015.png ; $\rho = \sum \lambda _ { i } P _ { i } , \quad 0 \leq \lambda _ { i } \leq 1 , \sum \lambda _ { i } = 1$ ; confidence 0.991

242. y1200107.png ; $R _ { 13 } = ( 1 \otimes _ { k } \tau _ { V , V } ) ( R \otimes _ { k } 1 ) ( 1 \otimes _ { k } \tau _ { V , V } )$ ; confidence 0.752

243. a130050146.png ; $\zeta _ { G } ( z ) = \sum _ { x = 1 } ^ { \infty } G ( n ) n ^ { - z } = \sum _ { \alpha \in G } | a | ^ { - z } =$ ; confidence 0.334

244. a12005039.png ; $S _ { \theta _ { 0 } } = \{ z \in C : \operatorname { larg } z | \leq \theta _ { 0 } \} \cup \{ 0 \}$ ; confidence 0.304

245. a12007019.png ; $| \frac { \partial U ( t , s ) } { \partial t } | | \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ]$ ; confidence 0.392

246. a12008063.png ; $\frac { d } { d t } \left( \begin{array} { l } { v _ { 0 } } \\ { v _ { 1 } } \end{array} \right) =$ ; confidence 0.779

247. a12017024.png ; $\int _ { 0 } ^ { + \infty } e ^ { - \lambda \alpha } \beta ( \alpha ) \Pi ( \alpha ) d \alpha = 1$ ; confidence 0.561

248. a1302308.png ; $\operatorname { lim } _ { n \rightarrow \infty } ( ( 1 - Q ) ( I - P ) ) ^ { n } f = ( I - P _ { U + V } ) f$ ; confidence 0.820

249. a12023021.png ; $\alpha _ { k } = \int _ { \Gamma } \frac { f ( \zeta ) d \zeta } { \zeta ^ { k + 1 } } , \quad k = 0,1$ ; confidence 0.846

250. b11066062.png ; $| K ( x , y ^ { \prime } ) - K ( x , y ) | \leq C | y ^ { \prime } - y | ^ { \gamma } | x - y | ^ { - n - \gamma }$ ; confidence 0.802

251. b110220137.png ; $c ( i , m ) L ( i , m ) = \operatorname { det } _ { Q } r _ { D } ( H _ { M } ^ { i + 1 } ( X , Q ( i + 1 - m ) ) _ { Z } )$ ; confidence 0.157

252. b12015058.png ; $\operatorname { lim } _ { n \rightarrow \infty } E _ { P } [ ( d _ { n } ^ { * } - d ^ { * } ) ^ { 2 } ] = 0$ ; confidence 0.582

253. b130120107.png ; $\omega ( f ^ { \prime } ; t ) _ { \infty } = O ( \operatorname { ln } \frac { 1 } { t } ) ^ { - 1 / 2 } )$ ; confidence 0.560

254. b12027048.png ; $\operatorname { lim } _ { t \rightarrow \infty } ( U ( t + h ) - U ( t ) ) = \frac { h } { E X _ { 1 } }$ ; confidence 0.762

255. b12032086.png ; $k \operatorname { log } m \leq i \operatorname { log } n < ( k + 1 ) \operatorname { log } r$ ; confidence 0.756

256. b13020070.png ; $\mathfrak { g } = \mathfrak { g } _ { + } \oplus \mathfrak { h } \oplus \mathfrak { g } _ { - }$ ; confidence 0.962

257. b13026061.png ; $\operatorname { deg } _ { B } [ f , \Omega , y ] = \operatorname { deg } _ { B } [ f , \Omega , z ]$ ; confidence 0.962

258. b13026058.png ; $\operatorname { deg } _ { B } [ f , \Omega , y ] = \operatorname { deg } _ { B } [ g , \Omega , y ]$ ; confidence 0.894

259. c130070246.png ; $\nu _ { 1 } ( 2 g _ { 1 } - 2 ) + \mathfrak { D } _ { 1 } = \nu _ { 2 } ( 2 g _ { 2 } - 2 ) + \mathfrak { D } _ { 2 }$ ; confidence 0.968

260. c13013010.png ; $A = \frac { \partial Q } { \partial L } \cdot \frac { 1 } { 1 - \alpha } \dot { k } ^ { - \alpha }$ ; confidence 0.216

261. c1301909.png ; $S = \operatorname { inv } ( N ) : = \{ x \in N : \varphi ( t , x ) \in \text { Nfor all } t \in R \}$ ; confidence 0.693

262. d03006011.png ; $u ( t , x ) | _ { t = 0 } = \phi ( x ) , \frac { \partial u ( t , x ) } { \partial t } | _ { t = 0 } = \psi ( x )$ ; confidence 0.969

263. d120020127.png ; $g ( \overline { u } _ { 1 } ) = c ^ { T } x ^ { ( l ) } + ( A _ { 1 } x ^ { ( l ) } - b _ { 1 } ) ^ { T } \overline { u }$ ; confidence 0.522

264. e12012094.png ; $d _ { i } ^ { ( t ) } = ( y _ { i } - \mu ^ { ( t ) } ) ^ { T } [ \Sigma ^ { ( t ) } ] ^ { - 1 } ( y _ { i } - \mu ^ { ( t ) } )$ ; confidence 0.846

265. e12002046.png ; $( X \wedge Z , Y ) \approx \operatorname { map } * ( X , \operatorname { map } _ { * } ( Z , Y ) )$ ; confidence 0.089

266. e12010044.png ; $t ^ { em } = t ^ { em } + ( P \otimes E ^ { \prime } - B \otimes M ^ { \prime } + 2 ( M ^ { \prime } B ) 1 )$ ; confidence 0.275

267. f12021083.png ; $= \frac { ( m _ { j } + l ) ! } { l ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { j } } + \ldots$ ; confidence 0.700

268. h13002080.png ; $( \alpha _ { 1 } , \alpha _ { 2 } , \dots , \alpha _ { q } \cup \gamma ^ { d } ) \in F ( S ^ { d } ) ^ { q }$ ; confidence 0.504

269. h11001017.png ; $S _ { f } ( \alpha ) = \sum _ { p } 1 / p \cdot ( 1 - \operatorname { Re } ( f ( p ) p ^ { - i \alpha } ) )$ ; confidence 0.571

270. h120020105.png ; $\int _ { D } | \psi ^ { ( n ) } ( \zeta ) | ^ { p } ( 1 - | \zeta | ) ^ { n p - 2 } d m _ { 2 } ( \zeta ) < \infty$ ; confidence 0.932

271. h12002032.png ; $\operatorname { lim } _ { | | \rightarrow 0 } \frac { 1 } { | T | } \int _ { I } | f - f _ { I } | d m = 0$ ; confidence 0.276

272. i13001042.png ; $\overline { d } ( n ) ( A ) = \operatorname { per } ( A ) \geq \overline { d } _ { \lambda } ( A )$ ; confidence 0.524

273. i13006090.png ; $H ( t ) : = - \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } ( | f ( k ) | ^ { - 2 } - 1 ) e ^ { - i k t } d k$ ; confidence 0.844

274. k05507045.png ; $g = \sum g _ { \alpha \overline { \beta } } d z ^ { \alpha } \otimes d z \square ^ { \beta }$ ; confidence 0.694

275. l1200208.png ; $\phi _ { i j } : \phi _ { j } ( U _ { i } \cap U _ { j } ) \rightarrow \phi _ { i } ( U _ { i } \cap U _ { j } )$ ; confidence 0.906

276. l13006074.png ; $z _ { i } \equiv \alpha _ { i } z _ { i - 1 } + \ldots + a _ { i } z _ { i - r } ( \operatorname { mod } p )$ ; confidence 0.242

277. m12007013.png ; $M ( P ) = | \alpha _ { 0 } | \prod _ { k = 1 } ^ { \phi } \operatorname { max } ( | \alpha _ { k } | , 1 )$ ; confidence 0.169

278. m1201901.png ; $F ( \tau ) = \frac { \pi } { 2 } \int _ { 0 } ^ { \infty } P _ { ( i \tau - 1 ) / 2 } ( 2 x ^ { 2 } + 1 ) f ( x ) d x$ ; confidence 0.458

279. m13022050.png ; $\left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) \in SL _ { 2 } ( Z )$ ; confidence 0.434

280. m13018035.png ; $g ( n ) = \sum _ { d | n } f ( d ) \Leftrightarrow f ( n ) = \sum _ { d | n } g ( d ) \mu ( \frac { n } { d } )$ ; confidence 0.878

281. n12010059.png ; $\| Y _ { m } \| _ { G } ^ { 2 } = \sum _ { i , j = 1 } ^ { k } g j \langle y _ { m } + i - 1 , y _ { m } + j - 1 \rangle$ ; confidence 0.187

282. n067520441.png ; $\dot { u } _ { i } = \tilde { \psi } _ { i } ( U ) + \tilde { \phi } _ { i } ( U ) , \quad i = 1 , \ldots , n$ ; confidence 0.234

283. o1300807.png ; $x \in R _ { + } , f _ { m } ( x , k ) = e ^ { i k x } + o ( 1 ) \operatorname { as } x \rightarrow + \infty$ ; confidence 0.151

284. q120070136.png ; $R ( t ^ { i } \square j \otimes t ^ { k } \square l ) = R ^ { i } \square j \square ^ { k } \square l$ ; confidence 0.278

285. r13004051.png ; $\mu _ { 2 } ( \Omega ) \leq ( \frac { 1 } { | \Omega | } ) ^ { 2 / n } C _ { n } ^ { 2 / n } p _ { n / 2,1 } ^ { 2 }$ ; confidence 0.369

286. r12002017.png ; $M _ { 11 } ( q ) \ddot { q } _ { 1 } + M _ { 12 } ( q ) \ddot { q } _ { 2 } + F _ { 1 } ( q , \dot { q } ) = \tau _ { 1 }$ ; confidence 0.991

287. s12016027.png ; $H ( q , d ) = \cup _ { q - d + 1 \leq | p | \leq q } ( X ^ { j _ { 1 } } \times \ldots \times X ^ { j _ { d } } )$ ; confidence 0.106

288. s13053016.png ; $e = \frac { | U | } { | G | } ( \sum _ { b \in B } b ) ( \sum _ { w \in W } \operatorname { sign } ( w ) w )$ ; confidence 0.138

289. s12026065.png ; $\{ A , A _ { s } ^ { * } \} = \delta ( t - s ) , \{ A _ { t } , A _ { s } \} = \{ A _ { t } ^ { * } , A _ { s } ^ { * } \} = 0$ ; confidence 0.760

290. s1306403.png ; $a _ { n } = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } a ( e ^ { i \theta } ) e ^ { - i n \theta } d \theta$ ; confidence 0.839

291. t13014044.png ; $X \mapsto \operatorname { dim } X = ( \operatorname { dim } _ { K } X _ { j } ) _ { j \in Q _ { 0 } }$ ; confidence 0.819

292. t130140119.png ; $\operatorname { dim } _ { 1 } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.287

293. t12021078.png ; $t ( M ; x , y ) = \sum _ { S \subseteq E } ( \prod _ { e \in S } p ( e ) ) ( \prod _ { e \in S } ( 1 - p ( e ) ) )$ ; confidence 0.241

294. t12021039.png ; $\chi ( G ; \lambda ) = \lambda ^ { \ell ( G ) } ( - 1 ) ^ { v ( G ) - c ( G ) } t ( M _ { G } , 1 - \lambda , 0 )$ ; confidence 0.067

295. w12002021.png ; $l _ { 1 } ( P , Q ) = \operatorname { sup } \{ \int f d ( P - Q ) : \operatorname { Lip } f \leq 1 \}$ ; confidence 0.358

296. z13010064.png ; $\exists x ( \emptyset \in x \wedge \forall y ( y \in x \rightarrow y \cup \{ y \} \in x ) )$ ; confidence 0.260

297. z13011095.png ; $= \frac { ( 1 - \alpha ) } { \dot { k } + c m _ { k } } . [ ( i - 1 + c ) \mu ( i - 1 , m ) - ( i + c ) \mu ( i , m ) ] +$ ; confidence 0.299

298. a130050215.png ; $\sum _ { n \leq x } S ( n ) = A _ { 2 } x + O ( \sqrt { x } ) \quad \text { as } x \rightarrow \infty$ ; confidence 0.344

299. a130050206.png ; $\sum _ { n \leq x } G _ { K } ( n ) = A _ { K } x + O ( x ^ { \eta } K ) \text { as } x \rightarrow \infty$ ; confidence 0.498

300. a13006075.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { P ^ { \# } ( n ) } { G ^ { \# } ( n ) } = 1$ ; confidence 0.848

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/6. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/6&oldid=44494