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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0969482-4
PII: S 0025-5718(1989)0969482-4
Article copyright: © Copyright 1989 American Mathematical Society