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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: one quadratic factor
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by B. C. Carlson PDF
Math. Comp. 56 (1991), 267-280 Request permission


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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Math. Comp. 56 (1991), 267-280
  • MSC: Primary 33E05; Secondary 65A05
  • DOI:
  • MathSciNet review: 1052087