A table of elliptic integrals: cubic cases

Author:
B. C. Carlson

Journal:
Math. Comp. **53** (1989), 327-333

MSC:
Primary 65A05; Secondary 33A25, 65D20

MathSciNet review:
969482

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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.

**[1]**Paul F. Byrd and Morris D. Friedman,*Handbook of elliptic integrals for engineers and scientists*, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York-Heidelberg, 1971. Second edition, revised. MR**0277773****[2]**B. C. Carlson,*A table of elliptic integrals of the second kind*, Math. Comp.**49**(1987), no. 180, 595–606, S13–S17. MR**906192**, 10.1090/S0025-5718-1987-0906192-1**[3]**B. C. Carlson,*A table of elliptic integrals of the third kind*, Math. Comp.**51**(1988), no. 183, 267–280, S1–S5. MR**942154**, 10.1090/S0025-5718-1988-0942154-7**[4]**I. S. Gradshteyn & I. M. Ryzhik,*Table of Integrals, Series, and Products*, Academic Press, New York, 1980.**[5]**A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev,*Integrals and series. Vol. 1*, Gordon & Breach Science Publishers, New York, 1986. Elementary functions; Translated from the Russian and with a preface by N. M. Queen. MR**874986**

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0969482-4

Article copyright:
© Copyright 1989
American Mathematical Society