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

 

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
MathSciNet review: 0175286
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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 (15,702a)
  • [2] 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 (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 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 0107353 (21 #6078)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1965-0175286-9
PII: S 0025-5718(1965)0175286-9
Article copyright: © Copyright 1965 American Mathematical Society