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Mathematics of Computation

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A table of elliptic integrals of the second kind

Author: B. C. Carlson
Journal: Math. Comp. 49 (1987), 595-606
MSC: Primary 65A05; Secondary 33A25, 65V05
MathSciNet review: 906192
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Abstract: 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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Article copyright: © Copyright 1987 American Mathematical Society