is represented as the sum of a convergent power series (also denoted by $ f _ {i} $
...expressed by the following properties of these series, regarded as formal power series in $ 2n $
10 KB (1,553 words) - 22:16, 5 June 2020
is the [[pointwise operation|pointwise]] sum and
...ormal Dirichlet series over $\mathbb{C}$ is isomorphic to a ring of formal power series in countably many variables.
2 KB (358 words) - 17:25, 11 November 2023
...residue formula one usually understands an integral representation for the sum of the values of a holomorphic function at all the zeros of a holomorphic m
...n - 1 ) ! } { ( 2 \pi i ) ^ {n } } \int _ { \partial D } \varphi \frac { \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } w _ { k } d w [ k ] \wedge d f } {
7 KB (1,090 words) - 10:25, 16 March 2024
...[[Fabry theorem|Fabry theorem]] on gaps; [[Lacunary power series|Lacunary power series]].
\sum _ { j= 1} ^ { k } L _ {ij} u _ {j} ,\ 1 \leq i \leq k ,
6 KB (898 words) - 14:30, 8 January 2022
...number and a left-part number of the other, whereas the right part of the sum consists of the sums of one number and a right part of the other.
...presentations of the surreal numbers which can be given in terms of formal power series over an index "set" which is isomorphic to the surreal numbers the
8 KB (1,226 words) - 16:11, 3 July 2016
in the form of a power series $ \Pi ( z _ {1} ; r ) = \sum _ {\nu = 0 } ^ \infty c _ \nu ( z - z _ {1} ) ^ \nu $
3 KB (399 words) - 22:17, 5 June 2020
...lane (except, possibly, at the point at infinity). It can be expanded in a power series
\sum _ {k = 0 } ^ \infty a _ {k} z ^ {k} ,\ \
8 KB (1,251 words) - 20:13, 10 January 2021
X = \sum _ {i = 1 } ^ { m }
...B.L. van der Waerden, "Order tests for the two-sample problem and their power" ''Proc. Kon. Nederl. Akad. Wetensch. A'' , '''55''' (1952) pp. 453–45
3 KB (401 words) - 08:27, 6 June 2020
\sum _ { n=1 } ^ \infty a _ {n} e ^ {- \lambda _ {n} s } ,
\sum _ { n=1 } ^ \infty
11 KB (1,638 words) - 11:32, 16 April 2023
...are [[elementary symmetric function]]s and $p_k(x_1,x_2,\ldots)$ are power sum symmetric functions. The algebraic structure underlying both identities is
...ence $(x_1,x_2,\ldots)$, then the $(k+1)$-st term in $P(x^n)$ is the power sum symmetric function $x_1^n+\cdots+x_k^n$ and the $k$-th term in $P(xP(\ldots
6 KB (960 words) - 07:40, 18 November 2023
or is a power of the characteristic $ p $
[ L:K ] \geq \sum _ {i = 1 } ^ { m } e ( w _ {i} \mid v ) \cdot f ( w _ {i} \mid w ) .
5 KB (827 words) - 17:32, 5 June 2020
the coefficients of these series are convergent power series in $ q $,
\sum _{n=1} ^ \infty \left [ 2 ^ {n+1}
3 KB (379 words) - 16:31, 6 January 2024
and is called the $ p $-th Pontryagin power $ {\mathcal P} _ {p} $.
\left ( \sum _ { i= 1} ^ { p- 1 }
6 KB (870 words) - 10:04, 11 July 2022
...e function $\phi(m)/m$ is a strongly multiplicative arithmetic function, a power function $m^k$ is a totally multiplicative arithmetic function.
3 KB (419 words) - 20:15, 19 November 2017
f ( z ) = \sum _ { k=0 } ^ \infty c _ {k} ( z - a ) ^ {k}
as a power series along all possible rays from the centre $ a $
5 KB (749 words) - 19:11, 19 June 2020
th exterior power of the space $ V $.
th exterior power $ \wedge ^ {r} M $,
7 KB (1,013 words) - 19:38, 5 June 2020
$ \sum _ {i} \pi _ {i} = 1 $,
where $ a _ {i} = \sum _ {j} n _ {i.ij } $
5 KB (733 words) - 06:29, 30 May 2020
...'(0,0)$ is a natural number) has a unique solution in the form of a formal power series:
...solution $y=\xi(x)$ of equation \eqref{1} cannot be proved by any partial sum of the Taylor series of $f$ (cf. [[#References|[2]]], [[#References|[3]]]).
2 KB (376 words) - 17:27, 14 February 2020
...s an injective object, and each injective object is isomorphic to a direct sum of indecomposable injective objects; this representation is moreover unique
...pos]] an object is injective if and only if it occurs as a retract of some power-object, and injective objects are used in the study of the associated sheaf
4 KB (643 words) - 22:12, 5 June 2020
Taking the direct sum of the internal space $ S _ {k} ( U) $
and the Hilbert sum of the central spaces there results a triplet
8 KB (1,190 words) - 08:16, 20 January 2024