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• Power series
  ...ccessive [[derivative]]s of the function: this [[Taylor series]] is then a power series in its own right. ...>a_n</math> be a sequence of real or complex coefficients. The associated power series is
  4 KB (785 words) - 14:27, 14 March 2021
• Power series/Definition
  152 bytes (20 words) - 17:21, 8 November 2008
• Power series/Bibliography
  302 bytes (38 words) - 17:25, 10 November 2008
• Formal power series
  #REDIRECT [[Power series#Formal power series]]
  46 bytes (6 words) - 13:23, 9 December 2008
• Power series/Related Articles
  635 bytes (94 words) - 17:06, 12 January 2010

Page text matches

• Formal power series
  #REDIRECT [[Power series#Formal power series]]
  46 bytes (6 words) - 13:23, 9 December 2008
• Power (disambiguation)
  {{rpl|Power series}}
  1 KB (178 words) - 13:34, 24 January 2023
• Radius of convergence
  #REDIRECT [[Power series#Radius of convergence]]
  48 bytes (6 words) - 14:46, 19 December 2008
• Puiseaux series/Related Articles
  {{rpl|Power series}}
  162 bytes (18 words) - 10:54, 26 July 2023
• Dirichlet series/Related Articles
  {{r|Power series}}
  436 bytes (54 words) - 11:42, 15 June 2009
• Series (analysis)/Related Articles
  {{r|Power series}}
  794 bytes (118 words) - 02:53, 7 November 2008
• Power series
  ...ccessive [[derivative]]s of the function: this [[Taylor series]] is then a power series in its own right. ...>a_n</math> be a sequence of real or complex coefficients. The associated power series is
  4 KB (785 words) - 14:27, 14 March 2021
• Formal group/Definition
  A formal power series behaving as if it were the product of a Lie group.
  109 bytes (18 words) - 07:51, 4 September 2009
• Weierstrass preparation theorem/Definition
  A description of a canonical form for formal power series over a complete local ring.
  121 bytes (18 words) - 15:11, 21 December 2008
• Fourier series/Related Articles
  {{r|Power series}}
  604 bytes (87 words) - 17:03, 12 January 2010
• Geometric series/Related Articles
  {{r|Power series}}
  213 bytes (24 words) - 16:16, 22 January 2010
• Weierstrass preparation theorem
  ...Weierstrass preparation theorem''' describes a canonical form for [[formal power series]] over a [[complete local ring]]. Let ''O'' be a complete local ring and ''f'' a formal power series in ''O''[[''X'']]. Then ''f'' can be written uniquely in the form
  745 bytes (116 words) - 13:35, 8 March 2009
• Generating function
  ...The ''ordinary generating function'' may be defined purely formally as a [[power series]] The ''exponential generating function'' may be defined similarly as a power series
  1 KB (148 words) - 13:24, 19 December 2009
• Holomorphic function/Proofs
  ...f in some open disk centered at ''a'' it can be expanded as a convergent [[power series]] * the fact that, since power series are infinitely differentiable, so are holomorphic functions (this is in con
  4 KB (730 words) - 15:17, 8 December 2009
• Dirichlet series
  ...s)|ring]]: an important special case is the ring of integers. A '''formal power series''' over ''R'', with variable ''S'' is a formal sum <math>\sum a_n n^{-S}</m
  2 KB (398 words) - 11:44, 15 June 2009
• Pole (complex analysis)
  ...nt series]] in a neighbourhood of ''a'', so that ''f'' is expressible as a power series
  1 KB (188 words) - 13:32, 8 March 2009
• Taylor series/Related Articles
  {{r|Power series}}
  993 bytes (129 words) - 20:50, 11 January 2010
• Formal group
  ...e a commutative ring. A '''formal group''' in one parameter is a [[formal power series]] <math>F\in A[[X,Y]]</math> such that
  602 bytes (121 words) - 13:24, 9 December 2008
• Theta function
  Jacobi's theta function is a [[power series]] in <math>\exp(\pi i \tau)</math> (traditionally referred to as the ''nome
  1 KB (161 words) - 04:13, 3 January 2009
• Geometric series
  == Geometric power series == ...t ''q'' by a variable ''x'' and consider the (real or complex) geometric [[power series]]
  7 KB (1,134 words) - 16:18, 22 January 2010
• Ring (mathematics)/Related Articles
  {{r|Power series}}
  1 KB (174 words) - 20:03, 11 January 2010
• Entire function
  ===Power series=== The [[radius of convergence]] of a [[power series]] is the distance the nearest [[singularity (mathematics)|singularity]]. T
  6 KB (827 words) - 14:44, 19 December 2008
• Function composition/Related Articles
  {{r|Power series}}
  749 bytes (92 words) - 16:43, 11 January 2010
• Calculus
  ===Power series of a function===
  5 KB (912 words) - 09:26, 29 May 2009
• Function (mathematics)
  ===Power series=== ...[[René Descartes]]), became tractable via such infinite sums now called [[power series]].<ref name=Arnold/>
  15 KB (2,342 words) - 06:26, 30 November 2011
• Series (mathematics)
  Most important are two classes of series of functions: [[power series|power]] (especially, [[Taylor series|Taylor]]) series whose terms are power
  19 KB (3,369 words) - 02:33, 13 January 2010
• Multipole expansion (interaction)
  This energy can be expanded in a power series&mdash; the '''multipole expansion'''&mdash;in the inverse distance of ''A'
  5 KB (902 words) - 08:21, 30 October 2008
• Fibonacci number
  ...'''Fibonacci generating function''' is defined as the sum of the following power series:
  5 KB (743 words) - 13:10, 27 July 2008
• Holomorphic function
  ...] of [[disk (mathematics)|disk]]s, centered at that point) as a convergent power series in the variables. This condition is stronger than the [[Cauchy-Riemann equa
  9 KB (1,434 words) - 15:35, 7 February 2009
• Derivative at a point
  ...heory|ring]] ''R''. Similarly we may define ''D'' on the ring of [[formal power series]] <math>R[[X]]</math>.
  5 KB (861 words) - 14:04, 23 February 2011
• Polynomial/Advanced
  ...llows one to view a polynomial ring as a [[subring]] of a [[ring of formal power series]]. This is the approach that will be used in this article.
  10 KB (1,741 words) - 10:04, 3 January 2009
• Number
  ...r]]s in 1897, looking for a way to bring the ideas and the techniques of [[power series]] within [[number theory]].
  11 KB (1,701 words) - 20:07, 1 July 2021
• Complex number
  ...math>z = i\theta</math> and comparing terms with the usual [[Taylor series|power series expansions]] of <math>\sin \theta</math> and <math>\cos \theta</math>.
  18 KB (3,028 words) - 17:12, 25 August 2013
• Gamma function
  ...extension in areas such as [[probability theory]] and the calculation of [[power series]]. Many expressions involving products of successive integers can be writte
  32 KB (5,024 words) - 12:05, 22 December 2008
• Complex number/Citable Version
  ...math>z = i\theta</math> and comparing terms with the usual [[Taylor series|power series expansions]] of <math>\sin \theta</math> and <math>\cos \theta</math>.
  20 KB (3,304 words) - 17:11, 25 August 2013
• Pascal's triangle
  ...someone found a remarkable equality between the Pascal's triangle and a [[power series]] of square [[matrix|matrices]].<ref>For instance, see Gottfried Helms, [ht
  32 KB (4,192 words) - 18:42, 3 March 2024
• Group (mathematics)
  [[Formal group law]]s are certain [[formal power series]] which have properties much like a group operation.
  19 KB (3,074 words) - 11:11, 13 February 2009
• History of number theory
  ...st of his work is restricted is restricted to the formal manipulation of [[power series]]. He did, however, do some very notable (though not fully rigorous) early
  35 KB (5,526 words) - 11:29, 4 October 2013