P E Falloon et al 2003 J. Phys. A: Math. Gen. 36 5477 doi:10.1088/0305-4470/36/20/309
P E Falloon, P C Abbott and J B Wang
Show affiliationsIn 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 and Schäfke (1954 Mathieusche Funktionen und Sphäroidfunktionen) and is available online (physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents 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 spheroidal wavefunctions of Flammer (1957 Spheroidal 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.
02.30.Lt Sequences, series, and summability
32A05 Power series, series of functions
33E10 Lamé, Mathieu, and spheroidal wave functions
65D20 Computation of special functions, construction of tables (See also 33F05)
Issue 20 (23 May 2003)
Received 20 December 2002, in final form 1 April 2003
Published 7 May 2003
P E Falloon et al 2003 J. Phys. A: Math. Gen. 36 5477
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