# 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.
References in periodicals archive ?
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.
8), the Jost solution E(*,z) has an analytic continuation from [D.
Applying the analytic continuation of the Helmholtz equation and Rellich's lemma [8, page 32, 33, 222], the solutions parameterized by k solve
Indeed, the inverse function may have an analytic continuation to A, with
1] (w) has an univalent analytic continuation to [absolute value of (w)] < 1.
Thus, by using such analytic continuation we get the r-ple gamma function
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 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.
1), and the final result follows by an appeal to the principle of analytic continuation.
Keywords Hexagon-number, Abel's summation formula, the analytic continuation.
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.
It can be shown by analytic continuation that when Im([omega]) < 0, the algebraic function [[xi].

Site: Follow: Share:
Open / Close