# analytic continuation

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## analytic continuation

[‚an·əl′id·ik kən·tin·yü′ā·shən]
(mathematics)
The process of extending an analytic function to a domain larger than the one on which it was originally defined.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Their topics include the Cauchy-Kovalevskaya theorem with estimates, applications of the Bony-Schapira theorem: Vekua Hulls and Szego's theorem revisited, potential theory on ellipsoids, singularities encountered by the analytic continuation of solutions to the Dirichlet problem, and quadrature domains and Laplacian growth.
Several authors have studied the analytic continuation of the multiple zeta function and proved that the multiple zeta function [zeta]([s.sub.1], ...,[s.sub.d]) of depth d can be analytically continued to a meromorphic function on all of [C.sup.d].
Application of principle of analytic continuation to (15) implies analytic continuation of the functions [[phi].sup.(0).sub.k] and [[phi].sup.(0).sub.0] (z) into all the domains [D.sub.k].
Zheng, "Multiplication operators on the Bergman space via analytic continuation," Advances in Mathematics, vol.
Under the condition (2.8), the Jost solution E(*,z) has an analytic continuation from [D.sub.0] to {z [member of] C : [absolute value of (z)] < 1} \{0}.
Indeed, the inverse function may have an analytic continuation to A, with
We now consider the function E(s) as the analytic continuation of Euler numbers.
By q-Euler zeta function, we consider the function [E.sub.q](s) as the analytic continuation of q-Euler numbers.
Analytic Continuation of (h, q)-Euler Numbers [E.sup.(h).sub.n,q]
where the function g is the analytic continuation of [f.sup.-1](w) to U.
of Oxford) introduces the constructive approximation of polynomials and rational functions, and extends the techniques to interpolation, quadrature, rootfinding, analytic continuation, extrapolation of sequence and series, and solution of differential equations.
The transfer rules also apply when there are finitely many singularities [[zeta].sub.1], ..., [[zeta].sub.l] on the boundary of the disk of convergence, provided analytic continuation holds in a [DELTA]-domain of the form [[zeta].sub.i] x [OMEGA] around each singularity.

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