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A code to evaluate prolate and oblate spheroidal harmonics. (English) Zbl 0937.65021

The authors present two FORTRAN 77 codes to evaluate prolate and oblate spheroidal harmonics. Subprogram specifications, performance of the codes, test runs and physical examples are included. The program is obtainable from QPC Program Library, Queen’s University of Belfast(Program title: DPROH, DOBLH; Catalog identifier ADHD).

MSC:

65D20 Computation of special functions and constants, construction of tables
33C55 Spherical harmonics
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References:

[1] Hobson, E. W., The theory of Spherical and Ellipsoidal harmonics (1965), Chelsea: Chelsea San Francisco, CA, ch. 5 · Zbl 0004.21001
[2] Lebedev, N. N., Special Functions & their Applications (1972), Dover: Dover New York, chs. 7, 8 · Zbl 0271.33001
[3] Gil, A.; Segura, J., Evaluation of Legendre functions of argument greater than one, Comput. Phys. Commun., 105, 273 (1997) · Zbl 0930.65010
[4] Abramowitz, M.; Stegun, J., (Handbook of Mathematical Functions (1972), Dover: Dover New York), ch. 8
[5] Gautschi, W., SIAM Rev., 9, 24-82 (1967)
[6] Thompson, I. J.; Barnett, A. R., J. Comput. Phys., 64, 490-509 (1986)
[7] Press, W. H.; Teukolski, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical Recipes in Fortran, ((1992), Cambridge Univ. Press: Cambridge Univ. Press New York), 257 ff, Section 6.11
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