A table of elliptic integrals: one quadratic factor

Author:
B. C. Carlson

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

MSC:
Primary 33E05; Secondary 65A05

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

MathSciNet review:
1052087

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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.

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

Article copyright:
© Copyright 1991
American Mathematical Society