...one of its sheets a largest open disc of radius $B_f > 0$. It was shown by A. Bloch [[#References|[1]]] that
A precise estimate for $B$ is
2 KB (312 words) - 17:31, 13 November 2016
...ve terms the value of which is not less than the values of all other terms of this series.
Applying this idea to the study of [[Power series|power series]]
1 KB (256 words) - 13:07, 12 December 2013
$#A+1 = 91 n = 0
$#C+1 = 91 : ~/encyclopedia/old_files/data/A010/A.0100460 Abstract analytic function,
6 KB (901 words) - 16:08, 1 April 2020
...a is sometimes used also for a useful property of sequences of subarhominc functions.
...\mathbb C$ is holomorphic at every point $\zeta\in D$ with respect to each variable $z_k$, then it is holomorphic with respect to all variables.
6 KB (1,001 words) - 18:22, 31 March 2017
...Ref|Ca}}||valign="top"| C. Caratheodory, "Theory of functions of a complex variable", '''1''', Chelsea (1983) Sects. 274–275
662 bytes (94 words) - 21:40, 27 April 2012
...arities]] of [[Holomorphic function|holomorphic functions]] of one complex variable
...o \mathbb C$ be an holomorphic function and $z_0$ a point for which $U$ is a punctured neighborhood. Then either the limit
3 KB (465 words) - 20:00, 14 December 2014
...n there exists at least one ray $S=\{z:\arg(z-a)=\theta_0\}$ issuing from $a$ such that in every angle
$$V=\{z:|\arg(z-a)-\theta_0|<\epsilon\},\quad\epsilon>0,$$
2 KB (343 words) - 21:49, 22 December 2018
...$-\infty\leqslant\alpha<\sigma<\beta\leqslant+\infty$, and expandable into a series
...\tau$ is called an $\varepsilon$-almost-period of $f(s)$ if for all points of the strip $(\alpha, \beta)$ the inequality
2 KB (348 words) - 06:21, 16 October 2013
...es was published by B. Taylor in 1715, whereas a series reducible to it by a simple transformation was published by Johann I. Bernoulli in 1694.
===One real variable===
4 KB (710 words) - 06:13, 13 June 2022
$#A+1 = 7 n = 0
A common singular point $ z _ {0} $
846 bytes (120 words) - 19:39, 5 June 2020
...|z|<1$ onto a [[Star-like domain|star-like domain]] with respect to $w=0$. A function $f(z)$, $f(z)\neq0$ in $0<|z|<1$, $f(0)=0$, $f'(0)\neq0$, regular
...ormalized so that $f(0)=0$, $f'(0)=1$, forms the class $S^*$, which admits a parametric representation by Stieltjes integrals:
3 KB (519 words) - 14:43, 30 July 2014
Formulas connecting the exponential and trigonometric functions:
These hold for all values of the complex variable $z$. In particular, for a real value $z=x$ the Euler formulas become
1 KB (171 words) - 12:50, 10 August 2014
$#A+1 = 1 n = 0
A mapping of one topological space into another under which the image of every open set is itself open.
3 KB (511 words) - 08:04, 6 June 2020
$#A+1 = 62 n = 0
A complex variable $ t $
5 KB (620 words) - 12:06, 9 December 2023
$#A+1 = 52 n = 0
...ent analytic functions in a complex domain. Suppose that the complement of a bounded continuum $ K $
5 KB (711 words) - 19:38, 5 June 2020
$#A+1 = 18 n = 0
$#C+1 = 18 : ~/encyclopedia/old_files/data/A012/A.0102510 Angular boundary value,
2 KB (293 words) - 18:47, 5 April 2020
...aginary parts of a complex-valued function $f$ of one (or several) complex variable so that $f$ is [[Holomorphic function|holomorphic]].
===One complex variable===
7 KB (1,063 words) - 12:51, 22 March 2023
...st partial fractions. Let $\{a_n\}_{n=1}^\infty$ be a sequence of distinct complex numbers,
and let $\{g_n(z)\}$ be a sequence of rational functions of the form
6 KB (980 words) - 18:47, 24 May 2017
...r integrals (cf. [[Fourier integral|Fourier integral]]), which are objects of harmonic analysis.
2 KB (287 words) - 11:59, 27 September 2012
$#A+1 = 25 n = 0
.../encyclopedia/old_files/data/B015/B.0105820 Besicovitch almost\AAhperiodic functions
4 KB (506 words) - 14:27, 30 May 2020