  In this paper we report on a package, written in the Mathematica computer
algebra system, which has been developed to compute the spheroidal wave
functions of Meixner [J. Meixner and R.W. Schaefke, Mathieusche Funktionen und
Sphaeroidfunktionen, 1954] and is available online
(www.physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package
represents a substantial contribution to the existing software, since it
computes the spheroidal wave functions to arbitrary precision for general
complex parameters mu, nu, gamma and argument z; existing software can only
handle integer mu, nu and does not give arbitrary precision. The package also
incorporates various special cases and computes analytic power series and
asymptotic expansions in the parameter gamma. The spheroidal wave functions of
Flammer [C. Flammer, Spheroidal Wave Functions, 1957] are included as a special
case of Meixner's more general functions. This paper presents a concise review
of the general theory of spheroidal wave functions and a description of the
formulas and algorithms used in their computation, and gives high-precision
numerical examples.
