A table of elliptic integrals: cubic cases

Carlson, B. C.

doi:10.1090/S0025-5718-1989-0969482-4

A table of elliptic integrals: cubic cases
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by B. C. Carlson PDF

Math. Comp. 53 (1989), 327-333 Request permission

Abstract:

Forty-one integrands that are rational except for the square root of a cubic polynomial with known real zeros are integrated in terms of R-functions for which Fortran codes are available. In contrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand. The table contains one elliptic integral of the first kind, 26 of the second kind, and 14 of the third kind. Only 10 of the integrals are treated in standard tables, which list a large number of special cases that are unified here.

References

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B. C. Carlson, A table of elliptic integrals of the second kind, Math. Comp. 49 (1987), no. 180, 595–606, S13–S17. MR 906192, DOI 10.1090/S0025-5718-1987-0906192-1
B. C. Carlson, A table of elliptic integrals of the third kind, Math. Comp. 51 (1988), no. 183, 267–280, S1–S5. MR 942154, DOI 10.1090/S0025-5718-1988-0942154-7

Table of Integrals, Series, and Products

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