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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] Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Bd LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642
  • [2] B. C. Carlson, Lauricella’s hypergeometric function 𝐹_{𝐷}, J. Math. Anal. Appl. 7 (1963), 452–470. MR 0157017, https://doi.org/10.1016/0022-247X(63)90067-2
  • [3] B. C. Carlson, Normal elliptic integrals of the first and second kinds, Duke Math. J. 31 (1964), 405–419. MR 0164067
  • [4] B. C. Carlson, On computing elliptic integrals and functions, J. Math. and Phys. 44 (1965), 36–51. MR 0175285
  • [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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