Calculation of the branch points of the eigenfunctions corresponding to wave spheroidal functions

A method for calculating eigenvalues λ^sub mn^(c) corresponding to the wave spheroidal functions in the case of a complex parameter c is proposed, and a comprehensive numerical analysis is performed. It is shown that some points c ^sub s^ are the branch points of the functions λ^sub mn^(c) with diff...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 46; no. 7; pp. 1132 - 1146
Main Authors: Skorokhodov, S. L., Khristoforov, D. V.
Format: Journal Article
Language:English
Published: Moscow Springer Nature B.V 01.07.2006
Subjects:
Analytic functions
Approximants
Bacteria
Eigenfunctions
Eigenvalues
Iterative methods
Mathematical analysis
Mathematical models
Numerical analysis
Studies
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:A method for calculating eigenvalues λ^sub mn^(c) corresponding to the wave spheroidal functions in the case of a complex parameter c is proposed, and a comprehensive numerical analysis is performed. It is shown that some points c ^sub s^ are the branch points of the functions λ^sub mn^(c) with different indexes n ^sub 1^ and n ^sub 2^ so that the value λ^sub mn^ ^sub 1^ (c ^sub s^) is a double one: λ^sub mn^ ^sub 1^ (c ^sub s^) = λ^sub mn^ ^sub 2^ (c ^sub s^). The numerical analysis suggests that, for each fixed m, all the branches of the eigenvalues λ^sub mn^(c) corresponding to the even spheroidal functions form a complete analytic function of the complex argument c. Similarly, all the branches of the eigenvalues λ^sub mn^(c) corresponding to the odd spheroidal functions form a complete analytic function of c. To perform highly accurate calculations of the branch points c ^sub s^ of the double eigenvalues λ^sub mn^(c ^sub s^), the Padé approximants, the Hermite-Padé quadratic approximants, and the generalized Newton iterative method are used. A large number of branch points are calculated.[PUBLICATION ABSTRACT]
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542506070049