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Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. (English) Zbl 0961.65017
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.
65D20Computation of special functions, construction of tables
33-04Machine computation, programs (special functions)
33C05Classical hypergeometric functions, 2 F 1
33C45Orthogonal polynomials and functions of hypergeometric type
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33C55Spherical harmonics