A table of elliptic integrals: one quadratic factor

Author:
B. C. Carlson

Journal:
Math. Comp. **56** (1991), 267-280

MSC:
Primary 33E05; Secondary 65A05

MathSciNet review:
1052087

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Integration in terms of real quantities is accomplished for 33 integrands that are rational except for the square root of a cubic or quartic polynomial with exactly one pair of conjugate complex zeros. Formulas are provided by which 45 more integrals of the same type can be expressed in terms of real quantities with the help of earlier papers. Neither limit of integration is assumed to be a singular point of the integrand. All the integrals are reduced to *R*-functions, for which Fortran programs are available. Most of the integrals are not listed in other tables.

**[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,*Elliptic integrals of the first kind*, SIAM J. Math. Anal.**8**(1977), no. 2, 231–242. MR**0430341****[3]**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**[4]**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**[5]**B. C. Carlson,*A table of elliptic integrals: cubic cases*, Math. Comp.**53**(1989), no. 187, 327–333. MR**969482**, 10.1090/S0025-5718-1989-0969482-4**[6]**B. C. Carlson,*Landen transformations of integrals*, Asymptotic and computational analysis (Winnipeg, MB, 1989) Lecture Notes in Pure and Appl. Math., vol. 124, Dekker, New York, 1990, pp. 75–94. MR**1052430****[7]**I. S. Gradshteyn and I. M. Ryzhik,*Table of integrals, series, and products*, Academic Press, New York, 1980.**[8]**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**

Retrieve articles in *Mathematics of Computation*
with MSC:
33E05,
65A05

Retrieve articles in all journals with MSC: 33E05, 65A05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052087-6

Article copyright:
© Copyright 1991
American Mathematical Society