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

Chebyshev approximations for the complete elliptic integrals $ K$ and $ E$


Author: W. J. Cody
Journal: Math. Comp. 19 (1965), 105-112
MSC: Primary 65.05
Corrigendum: Math. Comp. 20 (1966), 207.
MathSciNet review: 0171370
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Abstract | References | Similar Articles | Additional Information

Abstract: Chebyshev approximations of the Hastings form are given for the complete elliptic integrals $ K$ and $ E$. Maximal errors range from $ 4 \times {10^{ - 5}}$ down to $ 4 \times {10^{ - 18}}$.


References [Enhancements On Off] (What's this?)

  • [1] A. ErdÁlyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, v. II, McGraw-Hill, New York, 1953. MR 15, 419.
  • [2] J. R. Airey, "Toroidal functions and the complete elliptic integrals," Philos. Mag. (7), v. 19, 1935, p. 177-188.
  • [3] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, v. I, McGraw-Hill, New York, 1953. MR 15, 419.
  • [4] Cecil Hastings Jr., Approximations for digital computers, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR 0068915 (16,963e)
  • [5] W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions," Comm. ACM, v. 5, 1962, p. 401-403.
  • [6] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642 (29 #4914)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1965-0171370-4
PII: S 0025-5718(1965)0171370-4
Article copyright: © Copyright 1965 American Mathematical Society