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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A table of elliptic integrals of the second kind


Author: B. C. Carlson
Journal: Math. Comp. 49 (1987), 595-606, S13
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0906192-1
PII: S 0025-5718(1987)0906192-1
Article copyright: © Copyright 1987 American Mathematical Society