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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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  • 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
  • R. G. Selfridge and J. E. Maxfield, A table of the incomplete elliptic integral of the third kind, Dover Publications, Inc., New York, 1958. MR 0105827
  • L. V. King, On the Direct Calculation of Elliptic Functions and Integrals, Cambridge Univ. Press, New York, 1924. H. E. Salzer, "Quick calculation of the Jacobian elliptic functions," Comm. ACM, v. 5, 1962, no. 7.
  • A. R. DiDonato and A. V. Hershey, New formulas for computing incomplete elliptic integrals of the first and second kind, J. Assoc. Comput. Mach. 6 (1959), 515–526. MR 107353, DOI https://doi.org/10.1145/320998.321005

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Article copyright: © Copyright 1965 American Mathematical Society