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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 of the second kind
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by B. C. Carlson PDF
Math. Comp. 49 (1987), 595-606 Request permission


By evaluating elliptic integrals in terms of standard R-functions instead of Legendre’s integrals, many (in one case 144) formulas in previous tables are unified. The present table includes only integrals of the first and second kinds having integrands with real singular points. The 216 integrals of this type listed in Gradshteyn and Ryzhik’s table constitute a small fraction of the special cases of 13 integrals evaluated here. The interval of integration is not required, as it is in previous tables, to begin or end at a singular point of the integrand. Fortran codes for the standard R-functions are included in a Supplement.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 595-606
  • MSC: Primary 65A05; Secondary 33A25, 65V05
  • DOI:
  • MathSciNet review: 906192