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A table of elliptic integrals of the third kind. (English) Zbl 0647.33001

Math. Comput. 51, No. 183, 267-280 (1988); Supplement S1-S5 (1988).
Summary: 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.

MSC:

33E05 Elliptic functions and integrals
33C05 Classical hypergeometric functions, \({}_2F_1\)

Software:

algorithm 577
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Full Text: DOI

References:

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