A new method for computing toroidal harmonics

Fettis, Henry E.

doi:10.1090/S0025-5718-1970-0273786-6

A new method for computing toroidal harmonics
HTML articles powered by AMS MathViewer

by Henry E. Fettis PDF

Math. Comp. 24 (1970), 667-670 Request permission

Abstract:

A method for computing Legendre functions of integer order and half-odd degree is presented. The method is based on the theory of quadratic transformation of the argument, and is a generalization of Gauss’ or Landen’s transformation for computing elliptic integrals.

References

A. Rotenberg, The calculation of toroidal harmonics, Math. Comput. 14 (1960), 274–276. MR 0115264, DOI 10.1090/S0025-5718-1960-0115264-4

Brief Table of Ring Functions

Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002

Recent Developments in Recursive Computation

Henry E. Fettis, Calculation of toroidal harmonics without recourse to elliptic integrals, Blanch Anniversary Volume, Aerospace Research Lab., U.S. Air Force, Washington, D.C., 1967, pp. 21–34. MR 0211582
Henry E. Fettis and James C. Caslin, Tables of toroidal harmonics, I: Orders 0-5, all significant degrees. , Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1969. ARL 69-0025. MR 0245169
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York-London, 1965. Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin; Translated from the Russian by Scripta Technica, Inc; Translation edited by Alan Jeffrey. MR 0197789
Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629