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Theory and computation of spheriodal wavefunctions

P. E. Falloon
Organization: The University of Western Australia
Department: Physics
Paul Abbott
Organization: University of Western Australia
Department: Physics
URL: http://www.uwa.edu.au/people/paul.c.abbott
J. B. Wang
Organization: The University of Western Australia
Department: Physics
Journal / Anthology

Journal of Physics A
Year: 2003
Volume: 36
Page range: 5477-5495

Abstract: In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wavefunctions of Meixner (1954 Mathieusche Funktionen und Sphäroidfunktionen) and is available online (www.physics.uwa.edu.au/~falloon/spheroidal/spheriodal.html). This package respresents a substantial contribution to the existing software, since it computes the spheroidal wavefunctions to arbitrary precision for general complex parameters µ, ν, γ and argument z; existing software can only handle integer µ, ν and does not give arbitrary precision. The package also incorporates various special cases and computes analytic power series and asymptotic expansions in the parameter γ. The spherioidal wavefunctions of Flammer (1957 Spherioidal Wave functions) are included as a special case of Meixner's more general functions. This paper presents a concise review of the general theory of spheroidal wavefunctions and a description of the formulae and algorithms used in their computation, and gives high-precision numerical examples.

*Science > Physics > Thermodynamics and Statistical Mechanics