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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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A table of elliptic integrals: two quadratic factors
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by B. C. Carlson PDF
Math. Comp. 59 (1992), 165-180 Request permission


Thirteen integrands that are rational except for the square root of a quartic polynomial with two pairs of conjugate complex zeros are integrated in terms of R-functions of real variables. In contrast with previous tables, the formulas hold for all real intervals of integration for which the integrals exist (possibly as Cauchy principal values). This is achieved by using Landen’s transformation and the duplication theorem. In an appendix, an elliptic integral of the third kind with a restricted complex parameter is transformed to make the parameter real. Also, a degenerate integral of the first kind is separated into real and imaginary parts.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 165-180
  • MSC: Primary 65D20; Secondary 33C75, 33E05
  • DOI:
  • MathSciNet review: 1134720