analytic continuation


Also found in: Wikipedia.

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.
Mentioned in ?
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.
Linear Holomorphic Partial Differential Equations and Classical Potential Theory
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].
Analytic continuation of the multiple Fibonacci zeta functions
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].
Contrast Expansion Method for Elastic Incompressible Fibrous Composites
Zheng, "Multiplication operators on the Bergman space via analytic continuation," Advances in Mathematics, vol.
Restriction of Toeplitz Operators on Their Reducing Subspaces
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}.
SPECTRAL ANALYSIS OF A MATRIX-VALUED QUANTUM-DIFFERENCE OPERATOR
Indeed, the inverse function may have an analytic continuation to A, with
Coefficient Estimates for Certain Subclasses of Biunivalent Functions Defined by Convolution
We now consider the function E(s) as the analytic continuation of Euler numbers.
Analytic continuation of Euler polynomials and the Euler zeta function
By q-Euler zeta function, we consider the function [E.sub.q](s) as the analytic continuation of q-Euler numbers.
Zeros of analytic continued q-Euler polynomials and q-Euler zeta function
Analytic Continuation of (h, q)-Euler Numbers [E.sup.(h).sub.n,q]
Dynamics of the zeros of analytic continued (h, q)-Euler polynomials
where the function g is the analytic continuation of [f.sup.-1](w) to U.
Coefficient bounds for bi-starlike analytic functions
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.
Approximation theory and approximation practice
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.
Asymptotic enumeration of orientations

Encyclopedia browser ?
Full browser ?