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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Chebyshev approximations for the complete elliptic integrals $K$ and $E$
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by W. J. Cody PDF
Math. Comp. 19 (1965), 105-112 Request permission

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
    A. ErdÁlyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, v. II, McGraw-Hill, New York, 1953. MR 15, 419. J. R. Airey, "Toroidal functions and the complete elliptic integrals," Philos. Mag. (7), v. 19, 1935, p. 177–188. A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, v. I, McGraw-Hill, New York, 1953. MR 15, 419.
  • 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, DOI 10.1515/9781400875597
  • W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions," Comm. ACM, v. 5, 1962, p. 401–403.
  • Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Math. Comp. 19 (1965), 105-112
  • MSC: Primary 65.05
  • DOI: https://doi.org/10.1090/S0025-5718-1965-0171370-4
  • MathSciNet review: 0171370