Geodesic
Evaluation of associated Legendre functions off the cut and parabolic cylinder functions
Electronic transactions on numerical analysis, Tome 9 (1999), pp. 137-146
We review a set of algorithms to evaluate associated Legendre functions off the cut; in particular, we consider prolate spheroidal, oblate spheroidal and toroidal harmonics. A similar scheme can be applied to other families of special functions like Bessel and parabolic cylinder functions; we will describe the corresponding algorithm for the evaluation of parabolic cylinder functions.
Classification : 65D20, 33-04, 33C05, 33A70
Keywords: computation of special functions, Legendre functions, parabolic cylinder functions 
@article{ETNA_1999__9__a1,
     author = {Segura,  Javier and Gil,  Amparo},
     title = {Evaluation of associated {Legendre} functions off the cut and parabolic cylinder functions},
     journal = {Electronic transactions on numerical analysis},
     pages = {137--146},
     year = {1999},
     volume = {9},
     zbl = {0961.65017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1999__9__a1/}
}
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AU  - Gil,  Amparo
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EP  - 146
VL  - 9
UR  - http://geodesic.mathdoc.fr/item/ETNA_1999__9__a1/
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%A Segura,  Javier
%A Gil,  Amparo
%T Evaluation of associated Legendre functions off the cut and parabolic cylinder functions
%J Electronic transactions on numerical analysis
%D 1999
%P 137-146
%V 9
%U http://geodesic.mathdoc.fr/item/ETNA_1999__9__a1/
%G en
%F ETNA_1999__9__a1
Segura,  Javier; Gil,  Amparo. Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electronic transactions on numerical analysis, Tome 9 (1999), pp. 137-146. http://geodesic.mathdoc.fr/item/ETNA_1999__9__a1/