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- $#A+1 = 142 n = 2 ...edia/old_files/data/A013/A.0103000 Approximation of functions of a complex variable18 KB (2,637 words) - 07:20, 26 March 2023
- $#A+1 = 73 n = 0 ...edia/old_files/data/F042/F.0402120 Functions of a complex variable, theory of13 KB (1,922 words) - 19:55, 1 February 2022
Page text matches
- ...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 if2 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 functions3 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.encyclopediao4 KB (623 words) - 17:10, 7 February 2011
- $#A+1 = 24 n = 0 If a function3 KB (454 words) - 08:12, 6 June 2020
- $#A+1 = 19 n = 0 A function of the form2 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. Se2 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 plane2 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 (11 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 $\ln z$ ha3 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-holom705 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
- $#A+1 = 37 n = 0 Montel's theorem on the approximation of analytic functions by polynomials: If $ D $3 KB (452 words) - 12:08, 18 February 2022
- ''on conformal mapping of domains with variable boundaries'' ...$D_{z_0}$ is assumed to be bounded by a Jordan curve. Then the sequence of functions $\{w=f_n(z)\}$ which map $D_n$ conformally onto the disc $\Delta=\{w:|w|<1\1 KB (209 words) - 21:14, 22 December 2018
- ''exact radius of star-likeness, bound of star-likeness'' ...y number $r$ in the interval $0<r<R_U$ is called a radius of star-likeness of the class $U$.1 KB (245 words) - 08:26, 28 April 2023
- ''on uniform approximation by entire functions'' ...asing positive function $\epsilon(r)$, $0\leq r$ (as $r\to\infty$), having a positive lower bound on any finite interval, an entire function $g(z)$ such2 KB (243 words) - 18:27, 13 August 2015
- ...c continuation]] of a given element of an analytic function represented by a power series \Pi(a;r) = \sum_{\nu=0}^\infty c_\nu (z-a)^\nu2 KB (238 words) - 21:25, 13 December 2016
- ...on of the behaviour of specific functions. For the relief of the principal functions see [[#References|[2]]]. ...align="top">[2]</TD> <TD valign="top"> E. Jahnke, F. Emde, "Tables of functions with formulae and curves" , Dover, reprint (1945) (Translated from German930 bytes (137 words) - 11:16, 5 October 2014
- $#A+1 = 44 n = 0 $#C+1 = 44 : ~/encyclopedia/old_files/data/C025/C.0205040 Conjugate harmonic functions,4 KB (617 words) - 17:46, 4 June 2020
- ...n|analytic functions]] of one complex variable and sometimes in the theory of [[Partial differential equation|partial differential equations]]. ...$ is called a ''removable singular point'' of the function $f$ if there is a positive radius $r_0$ such that $f$ is bounded on the punctured disk $\{z:2 KB (344 words) - 08:39, 15 January 2014
- One of the [[Trigonometric functions|trigonometric functions]]: Its domain of definition is the entire real line; its range of values is the closed interval $[-1,1]$; the cosine is an even periodic func2 KB (283 words) - 12:43, 14 February 2020
- ...w D$, just as for every analytic function of one complex variable there is a corresponding [[Riemann surface]]; the function $f$ is single-valued on $\t ...D valign="top">[1]</TD> <TD valign="top"> B.V. Shabat, "Introduction of complex analysis" , '''2''' , Moscow (1976) (In Russian)</TD></TR>1 KB (205 words) - 17:02, 13 June 2020
- ...bharmonic function]]). For $n=1$ they correspond to logarithmically-convex functions. ...ve linear combination, of several logarithmically-subharmonic functions is a logarithmically-subharmonic function.1 KB (205 words) - 15:22, 29 December 2018
- $#A+1 = 40 n = 0 $#C+1 = 40 : ~/encyclopedia/old_files/data/A012/A.0102210 Analytic curve,3 KB (480 words) - 18:31, 5 April 2020
- $#A+1 = 52 n = 0 ''for an element of an analytic function $ f ( z) $''5 KB (764 words) - 22:13, 5 June 2020
- ''Riemann domain, complex (-analytic) manifold over $ \mathbf C ^{n} $'' An analogue of the [[Riemann surface|Riemann surface]] of an analytic function $ w = f(z) $4 KB (633 words) - 19:58, 28 January 2020
- ...als. Let $K$ be a compact subset of the complex $z$-plane $\mathbf C$ with a connected complement. Then every function $f$ continuous on $K$ and holomor ...eory in the complex plane and has many applications in various branches of complex analysis.5 KB (707 words) - 19:02, 1 May 2014
- ...www.encyclopediaofmath.org/legacyimages/i/i051/i051910/i0519105.png" /> of functions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l ...inside the respective domain) are also valid for other classes of analytic functions.6 KB (915 words) - 17:24, 7 February 2011
- Out of 36 formulas, 36 were replaced by TEX code.--> ...e } C ( X )$, where $A ^ { - 1 }$ is the family of invertible elements of $A$. Hypo-Dirichlet algebras were introduced by J. Wermer [[#References|[a4]]]3 KB (474 words) - 19:56, 27 February 2021
- The classical polylogarithms are special functions of a complex variable $z$, defined by the series ...umber inside the unit disk and $n$ an integer at least equal to $1$. These functions satisfy the differential equations2 KB (237 words) - 19:07, 1 May 2023
- $#A+1 = 52 n = 0 corresponding to the value of the argument $ x $,6 KB (901 words) - 12:10, 1 May 2023
- $#A+1 = 75 n = 0 ...percomplex function theory (cf. also [[Hypercomplex functions|Hypercomplex functions]]), renamed Clifford analysis in the 1980s, when it grew into an autonomous9 KB (1,297 words) - 17:44, 4 June 2020
- $#A+1 = 4 n = 0 of a complex variable $ z $,2 KB (240 words) - 08:18, 6 January 2024
- $#A+1 = 30 n = 0 ''branch point of infinite order''3 KB (399 words) - 22:17, 5 June 2020
- $#A+1 = 117 n = 0 $#C+1 = 117 : ~/encyclopedia/old_files/data/T094/T.0904210 Trigonometric functions12 KB (1,667 words) - 08:26, 6 June 2020
- The formula expressing the rule for raising a [[Complex number|complex number]], expressed in trigonometric form ...n $n$-th power. According to de Moivre's formula the modulus $\rho$ of the complex number is raised to that power and the argument $\varphi$ is multiplied by1 KB (241 words) - 10:03, 4 June 2013
- $#A+1 = 71 n = 0 ''of a Green function''6 KB (963 words) - 14:03, 18 May 2023
- $#A+1 = 29 n = 0 A single-valued analytic function $ f ( z) $4 KB (565 words) - 19:36, 5 June 2020
- $#A+1 = 18 n = 0 of the domain of definition $ D $2 KB (247 words) - 08:03, 6 June 2020
- ...arzian differential parameter, of an analytic function $f(z)$ of a complex variable $z$'' ...mal mapping]] of polygons onto the disc, in particular in the studies of H.A. Schwarz [[#References|[1]]].3 KB (443 words) - 11:10, 30 December 2018
- $#A+1 = 14 n = 0 The value of a function $ f ( z) $,2 KB (301 words) - 08:09, 6 June 2020
- ...Abel in {{Cite|Ab}}. If $a_1, \ldots, a_N$, $b_1, \ldots, b_N$, are given complex numbers and we set Observe that, if $B_0$ is arbitrarily chosen and we modify the definition of $B_n$ by2 KB (382 words) - 13:06, 10 December 2013