• mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds...
    20 KB (3,882 words) - 14:25, 25 July 2024
  • In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values...
    8 KB (1,030 words) - 20:59, 14 April 2024
  • Thumbnail for Monodromy theorem
    important result about analytic continuation of a complex-analytic function to a larger set. The idea is that one can extend a complex-analytic function (from...
    8 KB (1,331 words) - 14:39, 17 November 2023
  • arithmetic mean of the sequence of partial sums. Other methods involve analytic continuations of related series. In physics, there are a wide variety of summability...
    32 KB (5,028 words) - 01:29, 5 August 2024
  • Thumbnail for 1 + 2 + 3 + 4 + ⋯
    zeta function is that it can be defined for other values of s by analytic continuation. One can then define the zeta-regularized sum of 1 + 2 + 3 + 4 +...
    33 KB (4,228 words) - 10:38, 30 July 2024
  • Thumbnail for Wave packet
    In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope...
    35 KB (5,373 words) - 08:09, 7 August 2024
  • product expansion, it satisfies a functional equation, it has an analytic continuation to a meromorphic function on the complex plane C with only a simple...
    11 KB (1,593 words) - 21:16, 26 May 2024
  • Thumbnail for Spiral of Theodorus
    {\displaystyle f(0)=1,} and monotonicity in both argument and modulus. An analytic continuation of Davis' continuous form of the Spiral of Theodorus extends in...
    9 KB (1,157 words) - 18:15, 6 August 2024
  • bounded analytic function can become Analytic continuation, a technique to extend the domain of definition of a given analytic function Analytic manifold...
    5 KB (583 words) - 14:39, 20 March 2023
  • Thumbnail for Complex analysis
    the principle of analytic continuation which allows extending every real analytic function in a unique way for getting a complex analytic function whose...
    18 KB (2,517 words) - 14:08, 22 April 2024
  • Geometric function theory (category Analytic functions)
    function is conformal. Analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining...
    13 KB (1,787 words) - 15:31, 22 January 2024
  • Thumbnail for Gamma function
    \qquad \Re (z)>0\,.} The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic...
    90 KB (13,358 words) - 08:57, 13 August 2024
  • Thumbnail for L-function
    convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and some...
    8 KB (984 words) - 11:59, 7 May 2024
  • analysis, such as holomorphicity, the theory of algebraic curves, and analytic continuation. However, the numerical implementation is rather straightforward...
    18 KB (2,491 words) - 03:39, 11 February 2024
  • differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument...
    14 KB (2,056 words) - 11:01, 3 August 2024
  • Thumbnail for Riemann zeta function
    Riemann zeta function (category Analytic number theory)
    \operatorname {Re} (s)>1} , and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory, and has applications...
    68 KB (10,289 words) - 09:50, 15 August 2024
  • Thumbnail for Complex logarithm
    Complex logarithm (category Analytic functions)
    integration of 1 / z {\displaystyle 1/z} , or by the process of analytic continuation. There is no continuous complex logarithm function defined on all...
    28 KB (4,664 words) - 06:35, 6 July 2024
  • {\displaystyle z} . Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will...
    17 KB (2,729 words) - 18:14, 14 June 2024
  • complex functions, typically analytic functions. The domain to which a complex function may be extended by analytic continuation generally consists of almost...
    75 KB (11,265 words) - 19:54, 30 July 2024
  • greater than 1. It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex...
    10 KB (1,597 words) - 06:38, 22 July 2024
  • Thumbnail for Monodromy
    explicit in complex analysis. In the process of analytic continuation, a function that is an analytic function F(z) in some open subset E of the punctured...
    11 KB (1,459 words) - 17:57, 24 July 2024
  • {1}{1-z}}} which converges in the larger region Re(z) < 1, giving an analytic continuation of the original series. Considering instead the weak Borel transform...
    22 KB (3,511 words) - 22:49, 18 March 2024
  • The formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: Adding or subtracting two series term-by-term, Multiplying...
    11 KB (1,839 words) - 05:44, 27 November 2023
  • Thumbnail for Multivalued function
    originated in complex analysis, from analytic continuation. It often occurs that one knows the value of a complex analytic function f ( z ) {\displaystyle...
    9 KB (1,299 words) - 17:02, 17 July 2024
  • titled "On Integral Equations, Their Solution by Iteration and Analytic Continuation". In 1952, he participated in Project Whirlwind. He joined the faculty...
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  • Thumbnail for Schwarz reflection principle
    of definition of a complex analytic function, i.e., it is a form of analytic continuation. It states that if an analytic function is defined on the upper...
    3 KB (344 words) - 06:41, 7 January 2024
  • }}f^{(2k-1)}(x)} where C is a constant specific to the series and its analytic continuation and the limits on the integral were not specified by Ramanujan,...
    7 KB (1,364 words) - 22:44, 30 April 2024
  • p-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. The basic rigid analytic object...
    7 KB (985 words) - 19:08, 12 April 2022
  • Thumbnail for Casimir effect
    if the damping of large-frequency excitations corresponding to analytic continuation of the Riemann zeta function to s = 0 is assumed to make sense physically...
    63 KB (7,995 words) - 21:46, 14 August 2024
  • which aesthetically justifies this analytic continuation of the factorial function over any other analytic continuation. To the subject Lejeune Dirichlet...
    49 KB (5,993 words) - 20:23, 15 August 2024