$#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 $g(z)$ such
2 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)^\nu
2 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 German
930 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 func
2 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 equations
2 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 autonomous
9 KB (1,297 words) - 17:44, 4 June 2020