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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Recurrence relations for the indefinite integrals of the associated Legendre functions


Author: A. R. DiDonato
Journal: Math. Comp. 38 (1982), 547-551
MSC: Primary 33A45; Secondary 33A65
MathSciNet review: 645670
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Abstract | References | Similar Articles | Additional Information

Abstract: Two recurrence relations are derived for the computation of the integral of the associated Legendre functions of real argument and integer order and degree.


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

  • [1] Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774 (15,583h)
  • [2] M. K. Paul, Recurrence relations for integrals of associated Legendre functions, Bull. Géodésique 52 (1978), no. 3, 177–190. MR 0508198 (58 #22701)
  • [3] W. M. Robertson, Spherical Geodetic Transformations, Vol. I of II, Report No. R-l181, The Charles Stark Draper Laboratories, Inc., Cambridge, Mass. 02139, September 1978.
  • [4] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469 (97k:01072)
  • [5] B. Zondek, Aggregation Errors of Cell-Averaged Geoid Heights, Naval Surface Weapons Center, Dahlgren Laboratory, TR-3608, April 1977.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0645670-5
PII: S 0025-5718(1982)0645670-5
Article copyright: © Copyright 1982 American Mathematical Society