Search results

Page title matches

• Taylor series
  A '''Taylor series''' is an infinite sum of polynomial terms to approximate a function in the An intuitive explanation of the Taylor series is that, in order to approximate the value of <math>f(x)</math>, as a first
  5 KB (898 words) - 12:58, 11 June 2009
• Taylor series/Code
  36 bytes (3 words) - 00:47, 19 February 2009
• Taylor series/Definition
  158 bytes (24 words) - 20:21, 4 September 2009
• Taylor series/Approval
  12 bytes (1 word) - 01:27, 15 November 2007
• Taylor series/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Taylor series]]. Needs checking by a human.
  993 bytes (129 words) - 20:50, 11 January 2010
• Taylor series/Code/ExampleZ
  4 KB (774 words) - 00:46, 19 February 2009

Page text matches

• Maclaurin series
  #Redirect [[Taylor series]]
  27 bytes (3 words) - 04:02, 26 April 2007
• TaylorExampleZ/code
  #REDIRECT [[Taylor series/Code/ExampleZ]]
  41 bytes (5 words) - 00:46, 19 February 2009
• Taylor series
  A '''Taylor series''' is an infinite sum of polynomial terms to approximate a function in the An intuitive explanation of the Taylor series is that, in order to approximate the value of <math>f(x)</math>, as a first
  5 KB (898 words) - 12:58, 11 June 2009
• Generating function/Definition
  ...orresponding to a family of orthogonal polynomials ƒ0(x), ƒ1(x),…, where a Taylor series expansion of g(x,y) in powers of y will have the polynomial ƒn (x) as the
  250 bytes (42 words) - 08:09, 4 September 2009
• Binomial theorem/Related Articles
  {{r|Taylor series}}
  263 bytes (35 words) - 06:59, 15 July 2008
• Complex analysis/Related Articles
  {{r|Taylor series}}
  670 bytes (80 words) - 08:52, 7 August 2008
• Approximation theory/Related Articles
  {{r|Taylor series}}
  823 bytes (110 words) - 08:09, 22 September 2008
• Power series
  ...orm a power series from successive [[derivative]]s of the function: this [[Taylor series]] is then a power series in its own right. ...[analytic function]] of ''z''. Derivatives of all orders exist, and the [[Taylor series]] exists and is equal to the original power series.
  4 KB (785 words) - 14:27, 14 March 2021
• Taylor series/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Taylor series]]. Needs checking by a human.
  993 bytes (129 words) - 20:50, 11 January 2010
• Normal distribution/Related Articles
  {{r|Taylor series}}
  575 bytes (70 words) - 07:35, 16 April 2010
• Polygamma function
  ...ce the former is an entire function and hence has an everywhere convergent Taylor series in the simple point <math>z=0</math>, we can compute
  3 KB (488 words) - 10:34, 13 November 2007
• Derivative/Related Articles
  {{r|Taylor series}}
  572 bytes (72 words) - 02:47, 8 November 2008
• Holomorphic function/Proofs
  ...ormula for derivatives. Therefore the power series obtained above is the [[Taylor series]] of ''f''. ...ty|singularity]] of ''f''. Therefore the [[radius of convergence]] of the Taylor series cannot be smaller than the distance from ''a'' to the nearest singularity (
  4 KB (730 words) - 15:17, 8 December 2009
• Harmonic oscillator (classical)/Related Articles
  {{r|Taylor series}}
  652 bytes (82 words) - 17:05, 11 January 2010
• Holomorphic function/Related Articles
  {{r|Taylor series}}
  991 bytes (124 words) - 17:15, 11 January 2010
• Entire function/Related Articles
  {{r|Taylor series}}
  915 bytes (144 words) - 13:38, 19 December 2008
• Small angle approximation
  Mathematically, the small angle approximation is the first-order [[Taylor series|Maclaurin series]] of the sine function about the value zero. Recall Maclau
  2 KB (368 words) - 20:13, 29 January 2022
• Holomorphic function
  ...h function|infinitely often differentiable]] and can be described by its [[Taylor series]]. ...any function (real, complex, or of more general type) that is equal to its Taylor series in a neighborhood of each point in its domain. The fact that the class of '
  9 KB (1,434 words) - 15:35, 7 February 2009
• Entire function
  '''Any entire function can be expanded in every point to the [[Taylor series]] which [[convergence (series)|converges]] everywhere'''.
  6 KB (827 words) - 14:44, 19 December 2008
• Series (mathematics)
  ...two classes of series of functions: [[power series|power]] (especially, [[Taylor series|Taylor]]) series whose terms are power functions <math> c_n x^n </math> and Taylor and Fourier series behave quite differently. A Taylor series converges uniformly, together with all derivatives, on <math>[-a,a]</math>
  19 KB (3,369 words) - 02:33, 13 January 2010
• Harmonic oscillator (classical)
  It is of interest to show the connection with the [[Taylor series|Taylor expansion]] of an arbitrary potential around ''x''₀ Then the truncated Taylor series shrinks to
  11 KB (1,757 words) - 11:17, 11 September 2021
• Artin L-function
  ...rk conjectures]] predict that the coefficient of the leading term of the [[Taylor series]] expansion of an Artin L-function around ''s=0'' provides information abou
  2 KB (315 words) - 15:49, 10 December 2008
• Multipole expansion of electric field
  ...can be found in the literature; both will be given below. The first is a [[Taylor series]] in Cartesian coordinates, while the second is in terms of [[spherical ha The [[Taylor series|Taylor expansion]] of a function ''v''('''r'''-'''R''') around the origin '
  12 KB (1,953 words) - 04:38, 5 October 2009
• Electric dipole
  ...''V'' over the charge distribution. ''V'' is then given by a two-term [[Taylor series|Taylor expansion]],
  8 KB (1,270 words) - 18:42, 30 October 2021
• Lambert W function
  ...y, we find that the principal branch of the Lambert ''W'' function has the Taylor series expansion
  14 KB (2,354 words) - 21:43, 25 September 2011
• Factorial
  The [[radius of convergence]] of the Taylor series is unity, and the coefficient <math>g_n</math> does not decay as <math>n</m The Taylor series of <math>z!</math> developed at <math>z=1/2</math>, converges for all <math
  22 KB (3,358 words) - 09:31, 10 October 2013
• GF method
  ...he ''harmonic approximation''&mdash;on which the method is based&mdash;the Taylor series is ended after this quadratic term. The second term, containing first deriv
  13 KB (1,996 words) - 10:52, 3 November 2021
• Tetration/Code/TailorExpansion3ipower25
  // of the sum of the first 50 terms of the [[Taylor series]] for [[tetration]] developed at 3i.
  9 KB (1,245 words) - 00:39, 19 February 2009
• Complex number
  The same [[Taylor series|series]] may be used to define the ''complex'' exponential function ...substituting <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
  18 KB (3,028 words) - 17:12, 25 August 2013
• Trigonometric function
  ...ns|the significance of radians]] below.) One can then use the theory of [[Taylor series]] to show that the following identities hold for all [[real number]]s ''x'' ...o the trigonometric functions are defined on the complex numbers using the Taylor series above.
  33 KB (5,179 words) - 08:26, 4 June 2010
• Jacobian
  ...''m'' = 1, the Jacobi matrix appears in the second (linear) term of the [[Taylor series]] of ''f''. Here the Jacobi matrix is 1 &times; n (the [[gradient]] of ''f
  8 KB (1,229 words) - 08:32, 14 January 2009
• Pauli spin matrices
  as can be verified using the [[Taylor series]] expansion:
  7 KB (1,096 words) - 05:49, 17 October 2013
• Tetration
  The [[Taylor series]] for the tetration can be written in the usual form: The truncated Taylor series gives the [[polynomial approximation]].
  65 KB (10,203 words) - 04:16, 8 September 2014
• Complex number/Citable Version
  ...substituting <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
  20 KB (3,304 words) - 17:11, 25 August 2013
• Diabatic transformation
  The diabatic potential energy surfaces are smooth, so that low order [[Taylor series]] expansions of the surfaces may be applied and the expansions do not intro
  13 KB (1,922 words) - 07:19, 7 May 2010
• Polarizability
  ...generalized to higher powers in '''E''' (in the general case one uses a [[Taylor series]]), the polarizabilities arising as factors of E², and E<sup>3<
  12 KB (1,839 words) - 10:43, 5 October 2009
• Spherical harmonics
  as can be verified using the [[Taylor series]]:
  34 KB (5,282 words) - 14:21, 1 January 2011
• André-Marie Ampère
  ...hings he wrote about variational calculus and about the rest term of the [[Taylor series]] (1806).
  10 KB (1,656 words) - 01:58, 6 February 2010
• Newton's method
  ...fferentiable]] function in this region. Expanding <math>f(x)</math> in a [[Taylor series]] around <math>x = x_k</math> gives
  17 KB (2,889 words) - 12:40, 11 June 2009
• Magnetic moment
  as can be verified using the [[Taylor series]]:
  20 KB (3,045 words) - 11:21, 29 June 2011
• Intermolecular forces
  ...interatomic distance ''R''. Approximating the electronic interaction by a Taylor series in ''1/R'' he found an attractive potential with as leading term &minus;''C
  56 KB (8,720 words) - 07:31, 20 April 2024
• Normal distribution
  ...y accurately by a variety of methods, such as [[numerical integration]], [[Taylor series]], [[asymptotic series]] and [[continued fraction]]s.
  46 KB (6,956 words) - 07:01, 9 June 2009
• CZ Talk:Approval Process
  ...k was probably OK and a trivial decision but it's 40 years since I studied Taylor series) and that the articles had been through a thorough approval period, and tha
  96 KB (16,369 words) - 10:49, 7 March 2024
• Energy (science)
  Using the [[Taylor series]]
  43 KB (7,032 words) - 15:15, 15 August 2022