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.

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Zeta regularization is a method to treat the divergent quantities appearing in several areas of mathematics and physics, say Fermi and Pizzocchero, and these are managed by introducing a complex parameter, with the role of a regular, and defining their renormalized versions in terms of the analytic continuation with respect to the regulator.

Local Zeta Regularization and the Scalar Casimir Effect: A General Approach Based on Integral Kernels

8), the Jost solution E(*,z) has an analytic continuation from [D.

Spectral analysis of a matrix-valued quantum-difference operator

Applying the analytic continuation of the Helmholtz equation and Rellich's lemma [8, page 32, 33, 222], the solutions parameterized by k solve

Inverse uniqueness in interior transmission problem and its eigenvalue tunneling in simple domain

Indeed, the inverse function may have an analytic continuation to A, with

Coefficient Estimates for Certain Subclasses of Biunivalent Functions Defined by Convolution

1] (w) has an univalent analytic continuation to [absolute value of (w)] < 1.

Coefficient bounds for bi-starlike analytic functions

Thus, by using such analytic continuation we get the r-ple gamma function

Dualities for absolute zeta functions and multiple gamma 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 results of the present paper are related to the approximation of functions which are continuous on [0,1] and possess an analytic continuation into a disk {z : [absolute value of z] < a}, a > 0, by their q-Bernstein polynomials in the case q > 1.

On the approximation of analytic functions by the q-Bernstein polynomials in the case q > 1

1), and the final result follows by an appeal to the principle of analytic continuation.

New bilateral generating functions pertaining to the H-functions

Keywords Hexagon-number, Abel's summation formula, the analytic continuation.

On an infinite series related to Hexagon-numbers (1)

Emphasizing how complex analysis is a natural outgrowth of multivariable real calculus, this graduate textbook introduces the Cauchy integral formula, the properties and behavior of holomorphic functions, harmonic functions, analytic continuation, topology, Mergelyan's theorem, Hilbert spaces, and the prime number theorem.

Function Theory of One Complex Variable, 3d ed

It can be shown by analytic continuation that when Im([omega]) < 0, the algebraic function [[xi].

Transient Green's tensor for a layered solid half-space with different interface conditions