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Calculation of elliptic integrals of the third kind by means of Gauss' transformation


Author: Henry E. Fettis
Journal: Math. Comp. 19 (1965), 97-104
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1965-0175286-9
MathSciNet review: 0175286
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  • [1] Paul F. Byrd & Morris D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Springer, Berlin, 1954. MR 0060642 (15:702a)
  • [2] R. G. Selfridge & J. E. Maxfield, Table of the Incomplete Elliptic Integral of the Third Kind, Dover, New York, 1958. MR 0105827 (21:4562)
  • [3] L. V. King, On the Direct Calculation of Elliptic Functions and Integrals, Cambridge Univ. Press, New York, 1924.
  • [4] H. E. Salzer, "Quick calculation of the Jacobian elliptic functions," Comm. ACM, v. 5, 1962, no. 7.
  • [5] A. R. DiDonato & A. V. Hershey, "New formulae for computing incomplete elliptic integrals of the first and second kind," J. Assoc. Comput. Mach., v. 6, 1959, no. 4, p. 515-526. MR 0107353 (21:6078)

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DOI: https://doi.org/10.1090/S0025-5718-1965-0175286-9
Article copyright: © Copyright 1965 American Mathematical Society

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