Chebyshev approximations for the complete elliptic integrals 𝐾 and 𝐸-Reference-Cited by-同舟云学术

Chebyshev approximations for the complete elliptic integrals 𝐾 and 𝐸

Published:1965 Issue:89 Volume:19 Page:105-112
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Cody W. J.

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1965-19-089/S0025-5718-1965-0171370-4/S0025-5718-1965-0171370-4.pdf

Reference6 articles.

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. Approximations for Digital Computers

5. W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions," Comm. ACM, v. 5, 1962, p. 401–403.

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