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- ...rm '''''[[analytic function]]''''' is often used interchangeably with '''''holomorphic function''''', although the term '''''[[analytic function|analytic]]''''' is also us ...This is also because an important result in complex analysis is that every holomorphic function is complex analytic, a fact that does not follow directly from the definiti9 KB (1,434 words) - 15:35, 7 February 2009
- *is [[holomorphic function|holomorphic]] at a point ''a'' [[iff]] it is differentiable at every point4 KB (730 words) - 15:17, 8 December 2009
- 311 bytes (50 words) - 22:58, 17 February 2009
- Auto-populated based on [[Special:WhatLinksHere/Holomorphic function]]. Needs checking by a human.991 bytes (124 words) - 17:15, 11 January 2010
Page text matches
- ...unction (mathematics)|function]] is a point at which the function is not [[holomorphic function|holomorphic]], but which has a [[neighbourhood]] on which the function is h903 bytes (137 words) - 16:34, 11 November 2008
- {{rpl|Holomorphic function}}166 bytes (18 words) - 11:05, 24 January 2023
- A special function is often [[holomorphic function|holomorphic]] on some domain of the [[complex plane]]. Also, many special f716 bytes (101 words) - 16:51, 8 December 2009
- ...at a point ''a'' if there is a neighbourhood of ''a'' in which ''f'' is [[holomorphic function|holomorphic]] except at ''a'' and the limit <math>\lim_{z \rightarrow a} f(929 bytes (138 words) - 02:29, 25 October 2013
- '''Biholomorphism''' is a property of a [[holomorphic function|holomorphic]] [[function of a complex variable]]. ...ubseteq \mathbb{C} </math> is called ''biholomorphic'' if there exists a [[holomorphic function]] <math> g=f^{-1}</math> which is a two-sided [[inverse function]]: that is2 KB (293 words) - 17:36, 25 January 2009
- {{r|Holomorphic function}}993 bytes (129 words) - 20:50, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Holomorphic function]]. Needs checking by a human.991 bytes (124 words) - 17:15, 11 January 2010
- Property of a [[holomorphic function]] <math>f</math> from <math>A\subseteq \mathbb{C}</math> to <math> B \subse characterized in that there exist [[holomorphic function]] <math> g=f^{-1}</math>400 bytes (68 words) - 00:40, 2 February 2009
- In particular, every [[holomorphic function]] can be considered as meromorphic.839 bytes (128 words) - 10:05, 10 October 2013
- Holomorphic function characterized in that at integer values of its argument it can be interpret156 bytes (21 words) - 14:27, 8 March 2009
- ...f the [[complex plane]] is a [[function (mathematics)|function]] that is [[holomorphic function|holomorphic]] on all ''D'' ''except'' a set of [[isolated point]]s, which {{r|holomorphic function}}1 KB (215 words) - 03:15, 21 January 2009
- In complex analysis, the '''residue''' of a function ''f'' [[holomorphic function|holomorphic]] in an open set <math>\Omega</math> with possible exception of1 KB (227 words) - 16:56, 12 November 2008
- [[Superfunction]] of [[factorial]], [[holomorphic function|holomorphic]] solution <math>f</math> of equation605 bytes (85 words) - 01:42, 14 August 2009
- ...d singularity]]'' if there is a neighbourhood of ''a'' in which ''f'' is [[holomorphic function|holomorphic]] except at ''a''. In this case the function has a [[Laurent s1 KB (188 words) - 13:32, 8 March 2009
- {{r|Holomorphic function}}837 bytes (109 words) - 16:27, 11 January 2010
- ...</math> is [[holomorphic function]] on <math>C</math>, <math>f</math> is [[holomorphic function]] on <math>D</math>2 KB (305 words) - 11:03, 24 January 2023
- ...subsets]] of the half-plane <math> \Re (s) > 1 </math>. It thus defines a holomorphic function on this half-plane, and this can be extended by analytic continuation to a2 KB (343 words) - 07:23, 1 January 2009
- {{r|Holomorphic function}}774 bytes (100 words) - 18:05, 11 January 2010
- ...ents. Usually, the solution of a functional equation is supposed to be a [[holomorphic function]], although some functional equations were initially established for functi2 KB (215 words) - 00:05, 9 September 2009
- {{r|Holomorphic function}}1 KB (158 words) - 01:31, 14 August 2009
- {{r|Holomorphic function}}508 bytes (63 words) - 11:21, 11 January 2010
- ...rm '''''[[analytic function]]''''' is often used interchangeably with '''''holomorphic function''''', although the term '''''[[analytic function|analytic]]''''' is also us ...This is also because an important result in complex analysis is that every holomorphic function is complex analytic, a fact that does not follow directly from the definiti9 KB (1,434 words) - 15:35, 7 February 2009
- *is [[holomorphic function|holomorphic]] at a point ''a'' [[iff]] it is differentiable at every point4 KB (730 words) - 15:17, 8 December 2009
- {{r|Holomorphic function}}2 KB (206 words) - 19:38, 11 January 2010
- ...en mapping theorem for complex functions''. Let ''f'' be a non-constant [[holomorphic function]] on an open domain ''D'' in the [[complex plane]]. Then ''f'' is an open1 KB (179 words) - 17:30, 7 February 2009
- {{r|Holomorphic function}}930 bytes (136 words) - 07:49, 5 July 2011
- {{r|Holomorphic function}}477 bytes (61 words) - 19:12, 11 January 2010
- {{r|holomorphic function}}880 bytes (140 words) - 21:57, 25 September 2011
- {{r|Holomorphic function}}576 bytes (77 words) - 19:04, 11 January 2010
- ...ration. This approximation is especially recommended if the integrand is [[holomorphic function|holomorphic]] in a neighbourhood of integration interval. If the integrand is a [[holomorphic function]] along the path of integration, then the error of approximation decreases4 KB (630 words) - 12:32, 11 June 2009
- '''ArcSin''', or '''asign''', or '''arcsin''' is [[holomorphic function]], inverse of [[sine|sin]].5 KB (731 words) - 10:07, 2 December 2013
- an '''entire function''' is a [[function (mathematics)|function]] that is [[holomorphic function|holomorphic]] in the whole [[complex plane]]6 KB (827 words) - 14:44, 19 December 2008
- {{r|Holomorphic function}}908 bytes (142 words) - 06:59, 22 February 2011
- {{r|Holomorphic function}}918 bytes (144 words) - 02:40, 23 February 2011
- {{r|Holomorphic function}}972 bytes (150 words) - 16:38, 11 November 2008
- For the non–integer iterates, it should be assumed that <math>T</math> is [[holomorphic function]], and the superfunction <math>G</math> is also expected to be holomorphic. ...x) iterate of the transfer function <math>T</math> is straightforward; any holomorphic function can be declared as a [[transfer function]] and iterated any number of times15 KB (2,340 words) - 08:27, 9 September 2020
- For a [[holomorphic function]], the contour lines for the real part are orthogonal to those for the imag4 KB (567 words) - 00:52, 1 November 2013
- ...x variable then both <math> p(z)</math> and <math> 1/p(z)</math> will be [[holomorphic function|holomorphic]] in any domain where <math>\scriptstyle p(z) \ne 0</math>. But5 KB (924 words) - 16:35, 11 December 2008
- the Taylor series can be used to make the [[polynomial approximation]] of [[holomorphic function]]s, just truncating the series.5 KB (898 words) - 12:58, 11 June 2009
- ...more lucky than the <math>~\sqrt{!~}~~</math>; at least the existence of [[holomorphic function]] superfunction (from <math>a</math> to <math>b</math>) of [[holomorphic function]] <math>~f~</math> on domain <math>D</math> is21 KB (3,134 words) - 09:12, 10 October 2013
- ...subsets]] of the half-plane <math> \Re (s) > 1 </math>. It thus defines a holomorphic function on this half-plane, and this can be extended by analytic continuation to a7 KB (1,077 words) - 17:18, 10 January 2009
- ...d]] function of <var>2n</var> [[real number|real]] [[variable]]s to be a [[Holomorphic function|holomorphic one]]. They are named after [[Augustin-Louis Cauchy]] and [[Ber6 KB (874 words) - 03:45, 7 October 2013
- At base <math> b\!>\!1</math>, tetration is assumed to be a [[holomorphic function]], at least for positive values of the [[real part]] of its argument.65 KB (10,203 words) - 04:16, 8 September 2014
- ...discontinuity is called the ''cut'' of the logarithm. The logarithm is a [[holomorphic function]] on the complex plane except for the origin and the cut.19 KB (3,039 words) - 12:51, 7 March 2023