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Zbl 0961.65017
Segura, Javier; Gil, Amparo
Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. (English)
[J] ETNA, Electron. Trans. Numer. Anal. 9, 137-146, electronic only (1999). ISSN 1068-9613/e

The authors review a set of algorithms for evaluating the associated Legendre functions off the cut. In particular, they consider prolate spheroidal, oblate spheroidal and toroidal harmonics. Another family of functions that be computed in a similar wy are the parabolic cylinder functions. Aspects of forward and backward recursion schemes for computing solutions of three-term recursion relations are discussed. Numerical test of existing algorithms are also given.
[N.M.Temme (Amsterdam)]

MSC 2000:: *65D20 Computation of special functions
33-04 Machine computation, programs (special functions)
33C05 Classical hypergeometric functions
33C45 Orthogonal polynomials and functions of hypergeometric type
33C10 Cylinder functions, etc.
33C55 Elliptic integrals as hypergeometric functions

Keywords: computation of special functions; Legendre functions; parabolic cylinder functions; prolate spheroidal harmonics; oblate spheroidal harmonics; algorithms; toroidal harmonics; forward and backward recursion schemes; three-term recursion relations; numerical examples

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