A table of elliptic integrals: cubic cases-Reference-Cited by-同舟云学术

A table of elliptic integrals: cubic cases

Published:1989 Issue:187 Volume:53 Page:327-333
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Carlson B. C.

Abstract

Forty-one integrands that are rational except for the square root of a cubic polynomial with known real zeros are integrated in terms of R-functions for which Fortran codes are available. In contrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand. The table contains one elliptic integral of the first kind, 26 of the second kind, and 14 of the third kind. Only 10 of the integrals are treated in standard tables, which list a large number of special cases that are unified here.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1989-53-187/S0025-5718-1989-0969482-4/S0025-5718-1989-0969482-4.pdf

Reference5 articles.

1. Die Grundlehren der mathematischen Wissenschaften, Band 67;Byrd, Paul F.,1971

2. A table of elliptic integrals of the second kind;Carlson, B. C.;Math. Comp.,1987

3. A table of elliptic integrals of the third kind;Carlson, B. C.;Math. Comp.,1988

4. I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.

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