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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 third kind
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by B. C. Carlson PDF
Math. Comp. 51 (1988), 267-280 Request permission


As many as 72 elliptic integrals of the third kind in previous tables are unified by evaluation in terms of R-functions instead of Legendre’s integrals. The present table includes only integrals having integrands with real singular points. In addition to 31 integrals of the third kind, most of them unavailable elsewhere, 10 integrals of the first and second kinds from an earlier table are listed again in new notation. In contrast to conventional tables, the interval of integration is not required to begin or end at a singular point of the integrand. Fortran codes for the standard R-functions ${R_C}$ and ${R_J}$, revised to include their Cauchy principal values, are listed in a Supplement.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 267-280
  • MSC: Primary 33A25; Secondary 65A05
  • DOI:
  • MathSciNet review: 942154