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...

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...

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...

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

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

naturally in considering the possible analytic continuations of an analytic function, since analytic continuations may have a non-trivial monodromy. They...

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...

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

{\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...

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

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

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

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

{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...

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...

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...

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...

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

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

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...

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

integration of 1 / z {\displaystyle 1/z} , or by the process of analytic continuation. There is no continuous complex logarithm function defined on all...

0, it follows that g' (z)/g(z) has no singularities at zZ, and thus is analytic at zZ, which implies that the residue of f′(z)/f(z) at zZ is k. Let zP...

originated in complex analysis, from analytic continuation. It often occurs that one knows the value of a complex analytic function f ( z ) {\displaystyle...

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

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...