A table of elliptic integrals: one quadratic factor

Carlson, B. C.

doi:10.1090/S0025-5718-1991-1052087-6

A table of elliptic integrals: one quadratic factor
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Math. Comp. 56 (1991), 267-280 Request permission

Abstract:

Integration in terms of real quantities is accomplished for 33 integrands that are rational except for the square root of a cubic or quartic polynomial with exactly one pair of conjugate complex zeros. Formulas are provided by which 45 more integrals of the same type can be expressed in terms of real quantities with the help of earlier papers. Neither limit of integration is assumed to be a singular point of the integrand. All the integrals are reduced to R-functions, for which Fortran programs are available. Most of the integrals are not listed in other tables.

References

Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and scientists, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York-Heidelberg, 1971. Second edition, revised. MR 0277773
B. C. Carlson, Elliptic integrals of the first kind, SIAM J. Math. Anal. 8 (1977), no. 2, 231–242. MR 430341, DOI 10.1137/0508016
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
B. C. Carlson, A table of elliptic integrals: cubic cases, Math. Comp. 53 (1989), no. 187, 327–333. MR 969482, DOI 10.1090/S0025-5718-1989-0969482-4
B. C. Carlson, Landen transformations of integrals, Asymptotic and computational analysis (Winnipeg, MB, 1989) Lecture Notes in Pure and Appl. Math., vol. 124, Dekker, New York, 1990, pp. 75–94. MR 1052430

Table of integrals, series, and products

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and series. Vol. 1, Gordon & Breach Science Publishers, New York, 1986. Elementary functions; Translated from the Russian and with a preface by N. M. Queen. MR 874986