Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A new method for computing toroidal harmonics


Author: Henry E. Fettis
Journal: Math. Comp. 24 (1970), 667-670
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1970-0273786-6
MathSciNet review: 0273786
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. Rotenberg, "Calculation of toroidal harmonics," Math. Comp., v. 14, 1960, pp. 274-276. MR 22 #6066. MR 0115264 (22:6066)
  • [2] E. B. Wright & P. I. Peterson, Brief Table of Ring Functions, NRL Memorandum Report 1969, U. S. Naval Research Laboratory, March 1966.
  • [3] W. Gautschi, "Computational aspects of three-term recurrence relations," SIAM Rev., v. 9, 1967, pp. 24-82. MR 35 #3927. MR 0213062 (35:3927)
  • [4] J. Wimp, Recent Developments in Recursive Computation, ARL 69-0104, Aerospace Research Laboratories, July 1969.
  • [5] 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 35 #2460. MR 0211582 (35:2460)
  • [6] Henry E. Fettis & J. C. Caslin, Tables of Toroidal Harmonics, ARL 69-0025, Aerospace Research Laboratories, February 1969. MR 39 #6481. MR 0245169 (39:6481)
  • [7] I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965. MR 28 #5198; MR 33 #5952. MR 0197789 (33:5952)
  • [8] W. Magnus & F. Oberhetttnger, Formeln und Sätze für die Speziellen Funktionen der Mathematischen Physik, 2nd ed., Springer, Berlin, 1948; English transl., Chelsea, New York, 1949. MR 10, 38; MR 10, 532. MR 0025629 (10:38a)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.25

Retrieve articles in all journals with MSC: 65.25


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0273786-6
Keywords: Legendre functions, toroidal harmonics, quadratic transformations
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society