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 +...

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...

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

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...

\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...

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

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...

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

bounded analytic function can become Analytic continuation, a technique to extend the domain of definition of a given analytic function Analytic manifold...

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

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...

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

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

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

{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...

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...

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

}}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,...

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...

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

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

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

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...

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...