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Reduction and evaluation of elliptic integrals


Authors: W. J. Nellis and B. C. Carlson
Journal: Math. Comp. 20 (1966), 223-231
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1966-0215497-8
MathSciNet review: 0215497
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  • [1] P. F. Bybd & M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Die Grundlehren der mathematischen Wissenschaften, Bd. 67, Springer, Berlin, 1954. MR 15, 702. MR 0060642 (15:702a)
  • [2] B. C. Carlson, ``Lauricella's hypergeometric function $ F_d$,'' J. Math. Anal. Appl., v. 7, 1963, pp. 452-470. MR 28 #258. MR 0157017 (28:258)
  • [3] B. C. Carlson, "Normal elliptic integrals of the first and second kinds," Duke Math. J., v. 31, 1964, pp. 405-419. MR 29 #1360. MR 0164067 (29:1366)
  • [4] B. C. Carlson, "On computing elliptic integrals and functions," J. Math. and Phys., v. 44, 1965, pp. 36-51. MR 0175285 (30:5470)
  • [5] W. Gröbner & N. Hofreiter, Integraltafel, 2nd ed., Springer, Vienna, 1958.
  • [6] L. M. Milne-Thomson, "Elliptic integrals," M. Abramowitz & I. Stegun (Eds.), Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series, Vol. 55, U. S. Government Printing Office, Washington, D. C., 1964.
  • [7] W. J. Nellis, Tables of elliptic integrals, M. S. thesis, Iowa State University, Ames, Iowa, 1965.

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DOI: https://doi.org/10.1090/S0025-5718-1966-0215497-8
Article copyright: © Copyright 1966 American Mathematical Society

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