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  • Analysis (disambiguation)
    {{rpl|Complex analysis||**}}
    254 bytes (27 words) - 04:01, 26 September 2013
  • Several complex variables
    In [[mathematical analysis]], precisely in [[complex analysis]], '''several complex variables''' is the field that studies the properties
    198 bytes (26 words) - 06:52, 22 February 2011
  • Complex analysis/Related Articles
    ===Disciplines within complex analysis===
    670 bytes (80 words) - 08:52, 7 August 2008
  • Several complex variables/Definition
    Field of mathematics, precisely of [[complex analysis]], that studies those properties which characterize [[Function (mathematics
    232 bytes (27 words) - 04:54, 22 February 2011
  • Removable singularity
    In [[complex analysis]], a '''removable singularity''' is a type of [[singularity]] of a [[functi An isolated singularity may be either removable, a [[pole (complex analysis)|pole]], or an [[essential singularity]].
    929 bytes (138 words) - 02:29, 25 October 2013
  • Modular form/Definition
    <noinclude>{{Subpages}}</noinclude>A certain type of function in [[complex analysis]], with connections to [[algebraic geometry]] and [[number theory]]
    151 bytes (19 words) - 18:29, 15 December 2010
  • Cauchy-Riemann equations/Definition
    ...l equation]]s which characterize [[Function (mathematics)|functions]] in [[complex analysis]].
    160 bytes (18 words) - 05:17, 22 February 2011
  • Isolated singularity
    In [[complex analysis]], an '''isolated singularity''' of a [[complex number|complex]]-valued [[f ...er of ''z''-''a'' times ''f'' is bounded, and the singularity is a [[pole (complex analysis)|pole]].
    903 bytes (137 words) - 16:34, 11 November 2008
  • Residue (mathematics)/Related Articles
    {{r|Complex analysis}} {{r|Pole (complex analysis)}}
    560 bytes (69 words) - 20:00, 11 January 2010
  • Augustin-Louis Cauchy/Definition
    ...nent French mathematician, one of the pioneers of rigor in mathematics and complex analysis.
    149 bytes (17 words) - 13:55, 21 May 2008
  • Isolated singularity/Bibliography
    * {{cite book | author=Hilary A. Priestley | title=Introduction to Complex Analysis | edition=2nd ed | publisher=[[Oxford University Press]] | year=2003 | isbn
    189 bytes (24 words) - 16:43, 11 November 2008
  • Cauchy-Riemann equations/Related Articles
    {{r|Complex analysis}} {{r|Complex analysis}}
    918 bytes (144 words) - 02:40, 23 February 2011
  • Residue (mathematics)
    In complex analysis, the '''residue''' of a function ''f'' [[holomorphic function|holomorphic ...h>z_0</math> itself), with either a [[removable singularity]] or a [[pole (complex analysis)|pole]] at <math>z_0</math>, then it can be represented as a [[Laurent seri
    1 KB (227 words) - 16:56, 12 November 2008
  • Meromorphic functions/Related Articles
    ...] on all ''D'' ''except'' a set of [[isolated point]]s, which are [[pole (complex analysis)|pole]]s for the function. (The terminology comes from the [[Ancient Greek]
    1 KB (215 words) - 03:15, 21 January 2009
  • Several complex variables/Bibliography
    | title = An Introduction to Complex Analysis in Several Variables
    768 bytes (98 words) - 02:37, 23 February 2011
  • Algebraic surface
    ...'; part I in ''Global analysis'', Princeton university press. Part II in ''complex analysis and algebraic geometry'', Cambridge university press. Part III in ''Invent
    1,005 bytes (121 words) - 16:33, 1 December 2008
  • Classical control/Definition
    ...eveloped prior to the advent of state space methods, which rely heavily on complex analysis and transform methods, especially the Laplace and Fourier transforms, as we
    246 bytes (33 words) - 22:08, 11 September 2009
  • Riemann-Roch theorem/Definition
    Theorem that relates the complex analysis of a connected compact Riemann surface with the surface's purely topologica
    230 bytes (34 words) - 19:05, 4 September 2009
  • Pole (complex analysis)
    In [[complex analysis]], a '''pole''' is a type of [[singularity]] of a [[function (mathematics)|
    1 KB (188 words) - 13:32, 8 March 2009
  • Pole (disambiguation)
    {{rpl|Pole (complex analysis)}}
    166 bytes (21 words) - 05:56, 26 September 2013
  • Isolated singularity/Related Articles
    {{r|Complex analysis}} {{r|Pole (complex analysis)}}
    972 bytes (150 words) - 16:38, 11 November 2008
  • Cauchy-Riemann equations/Bibliography
    | title = An Introduction to Classical Complex Analysis. Vol. 1 }}. A comprehensive textbook on some topics of [[complex analysis]], with historical sections at the end of each chapter and also many histor
    2 KB (282 words) - 05:29, 8 February 2011
  • Several complex variables/External Links
    ...h to the theory. The authors are well known contributors to the field of [[complex analysis]].
    2 KB (237 words) - 08:05, 24 February 2011
  • Meromorphic functions
    In complex analysis, a meromorphic function on an open subset D of the complex plane is a funct
    839 bytes (128 words) - 10:05, 10 October 2013
  • Complex number/Related Articles
    {{r|Complex analysis}}
    276 bytes (34 words) - 10:41, 21 April 2010
  • Complex number/Bibliography
    |title = Complex Analysis
    899 bytes (119 words) - 17:42, 26 September 2007
  • Taylor series/Related Articles
    {{r|Complex analysis}}
    993 bytes (129 words) - 20:50, 11 January 2010
  • Complex analysis
    {{ dambigbox| Complex analysis | Analysis }} ...ing complex-valued functions does not qualify something for being called ''complex analysis''; it is really the new definitions of differentiation and integration with
    6 KB (1,077 words) - 19:25, 29 September 2020
  • Fundamental Theorem of Algebra
    ===Using complex analysis=== There are also proofs that do not depend on [[complex analysis]], but they require more [[algebra|algebraic]] or [[topology|topological]]
    5 KB (924 words) - 16:35, 11 December 2008
  • Generating function
    ...uence, allowing the application of methods of [[real analysis|real]] and [[complex analysis]] to problems in [[algorithmics]], [[combinatorics]], [[number theory]], [[
    1 KB (148 words) - 13:24, 19 December 2009
  • Littlewood polynomial
    ...Littlewood | authorlink=J. E. Littlewood | title=Some problems in real and complex analysis | publisher=D.C. Heath | year=1968 }}
    2 KB (230 words) - 16:13, 27 October 2008
  • Removable singularity/Related Articles
    {{r|Pole (complex analysis)}}
    505 bytes (63 words) - 19:58, 11 January 2010
  • Augustin-Louis Cauchy/Related Articles
    {{r|Complex analysis}}
    1 KB (162 words) - 07:35, 9 January 2011
  • Holomorphic function
    '''Holomorphic functions''' are the central object of study of [[complex analysis]]; they are [[function (mathematics)|functions]] defined on an [[open set|o ...oincides with the class of ''holomorphic functions'' is a major theorem in complex analysis.
    9 KB (1,434 words) - 15:35, 7 February 2009
  • Pole (complex analysis)/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Pole (complex analysis)]]. Needs checking by a human.
    665 bytes (81 words) - 19:37, 11 January 2010
  • Partial derivative/Related Articles
    {{r|Complex analysis}}
    663 bytes (84 words) - 19:23, 11 January 2010
  • Cauchy-Riemann equations
    In [[complex analysis]], the '''Cauchy-Riemann equations''' are one of the of the basic objects o ...ics]]<ref>See {{harvnb|D'Alembert|1752}}.</ref>: this connection between [[complex analysis]] and hydrodynamics is made explicit in classical [[treatise]]s of the latt
    6 KB (874 words) - 03:45, 7 October 2013
  • Integral/Related Articles
    {{r|Complex analysis}}
    763 bytes (99 words) - 17:28, 11 January 2010
  • Modular form
    A '''modular form''' is a type of function in [[complex analysis]], with connections to [[algebraic geometry]] and [[number theory]]. Modula
    1 KB (235 words) - 19:47, 15 December 2010
  • Holomorphic function/Related Articles
    {{r|Pole (complex analysis)}}
    991 bytes (124 words) - 17:15, 11 January 2010
  • Classical control
    ...man | Rudolf E. Kalman]]. The methods of classical control rely heavily on complex analysis and transform methods, especially the [[Laplace transform|Laplace]] and [[F
    862 bytes (114 words) - 05:54, 26 September 2007
  • Holomorphic function/Proofs
    In [[complex analysis]], a field of [[mathematics]], a [[complex number|complex]]-valued [[functi One of the most important theorems of complex analysis is that holomorphic functions are analytic. Among the corollaries of this
    4 KB (730 words) - 15:17, 8 December 2009
  • Several complex variables/Related Articles
    {{r|Complex analysis}}
    908 bytes (142 words) - 06:59, 22 February 2011
  • Calculus
    ...ed [[real analysis]] and the study of complex-valued functions is called [[complex analysis]].
    5 KB (912 words) - 09:26, 29 May 2009
  • Bernhard Riemann
    ...ician who made important contributions to [[differential geometry]], the [[complex analysis|theory of functions]], and [[number theory]].
    5 KB (751 words) - 11:37, 25 March 2022
  • Dirichlet character
    ...on]] with finitely many [[Euler factor]]s removed, and hence has a [[pole (complex analysis)|pole]] of order 1 at ''s''=1. Otherwise ''L''(''s'',χ) has a half-plane
    2 KB (335 words) - 06:03, 15 June 2009
  • Triangle inequality
    ...eory of [[normed vector space]]s in functional analysis, and in parts of [[complex analysis]].
    2 KB (414 words) - 08:12, 16 April 2009
  • Trigonometric function/Bibliography
    ...vca/PDF/vca-preface.pdf "Preface"]" to ''[http://www.usfca.edu/vca/ Visual Complex Analysis]''. Oxford University Press, (1999). ISBN 0-19-853446-9.
    2 KB (243 words) - 06:05, 22 May 2009
  • Prime Number Theorem
    ...used this to establish the prime number theorem. A proof not relying on [[complex analysis]] proved elusive, even though weaker results on the distribution of prime n
    4 KB (703 words) - 12:02, 13 November 2007
  • Complex number
    ...cially on [[complex analysis]]. But it is by no means necessary to rely on complex analysis here. A proof using [[field theory]] is alluded to at the very end of this
    18 KB (3,028 words) - 17:12, 25 August 2013
  • Number theory/Related Articles
    {{r|Complex analysis}}
    2 KB (262 words) - 19:07, 11 January 2010
  • Complex number/Citable Version
    ...cially on [[complex analysis]]. But it is by no means necessary to rely on complex analysis here. A proof using [[field theory]] is alluded to at the very end of this
    20 KB (3,304 words) - 17:11, 25 August 2013
  • Exponential function
    * Ahlfors, Lars V. (1953). Complex analysis. McGraw-Hill Book Company, Inc..
    6 KB (1,021 words) - 12:18, 11 June 2009
  • Wiener-Ikehara theorem
    ...ction|analytic]] for <math>\Re s \ge 1</math>, except for a simple [[Pole (complex analysis)|pole]] at <math>s=1</math> with residue 1. Then the [[Limit of a function|
    2 KB (362 words) - 16:05, 9 November 2008
  • Trigonometric function
    From a theorem in [[complex analysis]], there is a unique analytic extension of this real function to the comple ...rigonometric functions become essential in the geometric interpretation of complex analysis. For example, with the above identity, if one considers the unit circle in
    33 KB (5,179 words) - 08:26, 4 June 2010
  • Number theory
    the study of [[Complex analysis|analytical]] objects (e.g., the [[Riemann zeta function]]) that encode prop ...nt of much of modern mathematics necessary for basic modern number theory: complex analysis, group theory, Galois theory -- accompanied by greater rigor in analysis an
    27 KB (4,383 words) - 08:05, 11 October 2011
  • Lambert W function
    ...tically, despite its most important properties requiring only elementary [[complex analysis]]. An account of the function and its history that helped popularize it is
    14 KB (2,354 words) - 21:43, 25 September 2011
  • Gamma function
    ...nts due to division by zero; it is a [[meromorphic function]] with [[pole (complex analysis)|pole]]s at the nonpositive integers. The following image shows the graph o [[Karl Weierstrass]] further established the role of the gamma function in [[complex analysis]], starting from yet another product representation,
    32 KB (5,024 words) - 12:05, 22 December 2008
  • Augustin-Louis Cauchy
    This concept regards functions that have [[Pole (complex analysis)|poles]]&mdash;isolated singularities, i.e., points where a function goes t
    20 KB (3,286 words) - 12:52, 24 August 2013
  • Instrumentation for radioactivity
    There are limits to what can be determined with portable equipment. For more complex analysis, either a transportable laboratory needs to be brought to the site, or, if
    20 KB (2,892 words) - 16:53, 24 March 2024
  • Pole splitting
    ...between the input and output sides of the amplifier, the amplifier [[Pole (complex analysis)|pole]] lowest in frequency (usually an input pole) moves to a lower freque
    18 KB (3,162 words) - 09:46, 6 June 2011
  • Mathematics
    ..., one of the most fundamental open questions in mathematics, is drawn from complex analysis. [[Functional analysis]] focuses attention on (typically infinite-dimension
    30 KB (4,289 words) - 16:03, 20 January 2023
  • Syllable
    Internal evidence involves a more complex analysis of linguistic behaviour. For example, word [[stress (linguistics)|stress]]
    18 KB (2,729 words) - 14:12, 18 February 2024
  • Third Party System
    Gienapp (1987) is the most complex analysis of the formation of the system. His has six basic findings. First, the real
    25 KB (3,607 words) - 13:08, 9 August 2023
  • History of number theory
    ...inite series) in number theory. Since he lived before the development of [[complex analysis]], most of his work is restricted is restricted to the formal manipulation
    35 KB (5,526 words) - 11:29, 4 October 2013
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