...s of a complex variable, theory of|Functions of a complex variable, theory of]]).
423 bytes (68 words) - 16:59, 7 February 2011
''simple function (of a complex variable)''
...older, names for a [[Univalent function|univalent function]] of a complex variable.
659 bytes (91 words) - 17:05, 7 February 2011
''in the theory of functions of a complex variable''
If $f(z)$ is a regular analytic function in the disc $|z|<R$, $\alpha$ is a positive number, and if
2 KB (260 words) - 17:48, 1 November 2014
''in a domain''
...tion at a point $a$ is a function that is regular in some neighborhood of $a$.
537 bytes (80 words) - 21:41, 17 October 2014
...ons]] $\tan z$ and $\operatorname{cotan}z$ are meromorphic simply-periodic functions with fundamental period $2\omega=\pi$.
...riod $2\omega\in X$. A non-constant continuous periodic function of a real variable is necessarily simply-periodic.
897 bytes (128 words) - 18:55, 17 October 2014
$#A+1 = 24 n = 0
$#C+1 = 24 : ~/encyclopedia/old_files/data/I052/I.0502370 Inverse hyperbolic functions
3 KB (487 words) - 19:15, 17 January 2024
...ww.encyclopediaofmath.org/legacyimages/c/c026/c026420/c0264201.png" />,
of a function <img align="absmiddle" border="0" src="https://www.encyclopediaofm
...//www.encyclopediaofmath.org/legacyimages/c/c026/c026420/c02642011.png" />
of the domain <img align="absmiddle" border="0" src="https://www.encyclopediao
4 KB (623 words) - 17:10, 7 February 2011
$#A+1 = 24 n = 0
If a function
3 KB (454 words) - 08:12, 6 June 2020
$#A+1 = 19 n = 0
A function of the form
2 KB (328 words) - 19:37, 5 June 2020
...d on considering all possible elements of an analytic function in the form of generalized power series ([[Puiseux series]])
...table topology, the analytic image is converted to the [[Riemann surface]] of the given function.
1 KB (199 words) - 17:44, 1 November 2014
...ng all paths in an arbitrary domain $D\subset\mathbf C^n$, then the result of this continuation at any point $z^*\in D$ (that is, the element $\Sigma(z^*
The monodromy theorem is valid also for analytic functions $f(z)$ defined in domains $D$ on Riemann surfaces or on Riemann domains. Se
2 KB (315 words) - 10:59, 27 June 2015
$#A+1 = 12 n = 0
$#C+1 = 12 : ~/encyclopedia/old_files/data/E036/E.0306950 Extended complex plane
2 KB (233 words) - 19:38, 5 June 2020
...is an extremal function in a number of problems in the theory of univalent functions (cf. [[Bieberbach conjecture]]; [[Univalent function]]).
...]</TD> <TD valign="top"> W.K. Hayman, "Coefficient problems for univalent functions and related function classes" ''J. London Math. Soc.'' , '''40''' : 3 (1
1 KB (188 words) - 19:36, 5 April 2023
''in the theory of functions of a complex variable''
...t is necessary and sufficient that it be uniformly bounded in the interior of $D$, that is, uniformly bounded on any compactum $K\subset D$.
2 KB (306 words) - 13:06, 28 August 2014
...omorphic functions $f(z)$ in the space $\mathbf C^n$, $n\geq2$, of several complex variables $z=(z_1,\ldots,z_n)$.
...ranscendental function is the presence of either a singularity that is not a pole or an algebraic branch point; e.g. the logarithmic function $\ln z$ ha
3 KB (477 words) - 13:50, 9 April 2023
...phic function|holomorphic functions]] of one complex variable. In the case of the unit circle one has the following relationship between the Cauchy kerne
See also [[Kernel of an integral operator]].
1 KB (198 words) - 20:26, 18 March 2024
...of functions of a complex variable|Approximation of functions of a complex variable]]).
...ompact set $K\subset D$ and $\epsilon>0$ there is a polynomial $p(z)$ with complex coefficients such that $|f(z)-p(z)|<\epsilon$ for all $z\in K$.
3 KB (531 words) - 18:58, 1 May 2014
''conformal mapping of the second kind''
...gles between the curves passing through $z_0$ but changes the orientation. A function $f(z)$ which produces an anti-conformal mapping is an [[Anti-holom
705 bytes (104 words) - 15:14, 17 July 2014
''for a meromorphic function $f(z)$ in a domain $G$ of the complex $z$-plane''
...inside $D$ within any angle with vertex $\zeta$ formed by a pair of chords of $D$.
2 KB (264 words) - 21:15, 1 November 2014
...$ be valid; then in the domain $G$ the sum $f(z)+g(z)$ has the same number of zeros as $f(z)$.
...f the|Argument, principle of the]]) and it implies the fundamental theorem of algebra for polynomials.
3 KB (461 words) - 12:23, 14 February 2020