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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A table of elliptic integrals: cubic cases
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by B. C. Carlson PDF
Math. Comp. 53 (1989), 327-333 Request permission


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
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 327-333
  • MSC: Primary 65A05; Secondary 33A25, 65D20
  • DOI:
  • MathSciNet review: 969482