mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds...

In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values...

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...

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...

analysis, such as holomorphicity, the theory of algebraic curves, and analytic continuation. However, the numerical implementation is rather straightforward...

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 +...

The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is...

an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions...

the principle of analytic continuation which allows extending every real analytic function in a unique way for getting a complex analytic function whose...

p-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. The basic rigid analytic object...

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...

function is conformal. Analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining...

{\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...

titled "On Integral Equations, Their Solution by Iteration and Analytic Continuation". In 1952, he participated in Project Whirlwind. He joined the faculty...

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...

{\displaystyle 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...

explicit in complex analysis. In the process of analytic continuation, a function that is an analytic function F ( z ) {\displaystyle F(z)} in some open...

these points as branch points. The sum of these functions gives the analytic continuation of the bilateral hypergeometric series to all values of z other...

differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument...

them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions. Dimensional regularization...

respect to z at every point of U. Equivalently, it is holomorphic if it is analytic, that is, if its Taylor series exists at every point of U, and converges...

{\displaystyle z} . Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will...

complex functions, typically analytic functions. The domain to which a complex function may be extended by analytic continuation generally consists of almost...

z with |z| < 1; it can be extended to |z| ≥ 1 by the process of analytic continuation. (Here the denominator ks is understood as exp(s ln k)). The special...

on the edge. It is used in quantum field theory to construct the analytic continuation of Wightman functions. The formulation and the first proof of the...

{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...

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...

Another problem of extrapolation is loosely related to the problem of analytic continuation, where (typically) a power series representation of a function is...

\operatorname {Re} (s)>1} , and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory and has applications...

theory. A number of issues were clarified, in particular that of analytic continuation. Here a major difference is evident from the one-variable theory;...