$#A+1 = 136 n = 0
$#C+1 = 136 : ~/encyclopedia/old_files/data/R081/R.0801560 Residue of an analytic function
16 KB (2,407 words) - 07:56, 11 January 2022
A map $f:X \to Y$ is called invertible if for every $y\in Y$ there exists one
...uthors still use the notation $f^{-1} (y)$), and it consists of the subset of $X$ defined by
10 KB (1,719 words) - 16:56, 30 November 2014
$#A+1 = 107 n = 1
A function of complex variables with the reproducing kernel property, defined for any domain $
10 KB (1,514 words) - 07:41, 26 March 2023
$#A+1 = 23 n = 0
...sums of a series in a domain that is larger than the domain of convergence of the series. The following theorems on over-convergence hold:
3 KB (438 words) - 12:39, 6 January 2024
$#A+1 = 182 n = 3
A function of a complex variable $ s = \sigma + it $
15 KB (2,181 words) - 11:50, 26 March 2023
A complex number is a number of the form $z=x+iy$, where $x$ and $y$ are real numbers (cf.
that is, a number whose square is equal to $-1$ (in engineering
14 KB (2,281 words) - 09:55, 26 March 2023
$#A+1 = 55 n = 0
...by Yu.V. Sokhotskii [[#References|[1]]], expressing the boundary values of a Cauchy-type integral. With more complete proofs but significantly later, th
9 KB (1,249 words) - 14:55, 7 June 2020
$\def\a{\alpha}$
An abbreviated form of notation in analysis, imitating the vector notation by single letters rathe
3 KB (512 words) - 06:16, 13 June 2022
...braic equations: Formulas expressing the solution of an arbitrary equation of degree $ n $
in terms of its coefficients using radicals do not exist for any $ n \geq 5 $.
6 KB (894 words) - 06:14, 26 March 2023
$#A+1 = 68 n = 0
...cyclopedia/old_files/data/U095/U.0905160 Undetermined coefficients, method of
9 KB (1,382 words) - 08:27, 6 June 2020
$#A+1 = 25 n = 0
be a function realizing a univalent [[Conformal mapping|conformal mapping]] of the disc $ \{ {z \in \mathbf C } : {| z | < 1 } \} $
3 KB (486 words) - 01:08, 19 March 2022
$#A+1 = 87 n = 0
...function inside a domain if certain bounds on the modulus on the boundary of the domain are known [[#References|[1]]], [[#References|[2]]]. Let $ D $
8 KB (1,149 words) - 19:43, 5 June 2020
$#A+1 = 64 n = 0
...odic function|double-periodic function]] that is meromorphic in the finite complex $ z $-plane. An elliptic function has the following basic properties.
9 KB (1,292 words) - 19:08, 20 January 2022
$#A+1 = 67 n = 0
of all fractional-linear transformations $ \gamma $
7 KB (1,031 words) - 18:33, 13 January 2024
==Liouville's theorem on bounded entire analytic functions==
of the complex variable $ z = ( z _ {1}, \dots, z _ {n} ) $
8 KB (1,240 words) - 04:55, 24 February 2022
...of transformations]] $ \Gamma $ of analytic transformations of a given complex manifold $ M $ :
...that are invariant under a discrete group $ \Gamma $ of automorphisms of this domain.
17 KB (2,502 words) - 06:16, 12 July 2022
$#A+1 = 78 n = 0
$#C+1 = 78 : ~/encyclopedia/old_files/data/A010/A.0100120 Abel\ANDGoncharov problem,
9 KB (1,324 words) - 11:49, 10 April 2023
$#A+1 = 92 n = 1
A solution of a [[Hypergeometric equation|hypergeometric equation]]
12 KB (1,576 words) - 01:14, 21 January 2022
$#A+1 = 247 n = 0
A Cauchy integral is a definite integral of a continuous function of one real variable. Let $ f (x) $
26 KB (3,804 words) - 08:11, 13 February 2022
Out of 101 formulas, 101 were replaced by TEX code.-->
...intimately reflect complex-analytic/geometric properties of the boundaries of such domains.
15 KB (2,167 words) - 16:10, 11 February 2024