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...

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...

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...

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...

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...

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

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...

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

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

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...

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...

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...

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

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

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...

such that f ( z ) − R / ( z − a ) {\displaystyle f(z)-R/(z-a)} has an analytic antiderivative in a punctured disk 0 < | z − a | < δ {\displaystyle 0<\vert...

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

{\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...

{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...

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...

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...

In mathematics, the Fabry gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders that have...

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