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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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7.13.3 Legendre Form of Complete Elliptic Integrals

Function: double gsl_sf_ellint_Kcomp (double k, gsl_mode_t mode)
Function: int gsl_sf_ellint_Kcomp_e (double k, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the complete elliptic integral K(k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
Function: double gsl_sf_ellint_Ecomp (double k, gsl_mode_t mode)
Function: int gsl_sf_ellint_Ecomp_e (double k, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the complete elliptic integral E(k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
Function: double gsl_sf_ellint_Pcomp (double k, double n, gsl_mode_t mode)
Function: int gsl_sf_ellint_Pcomp_e (double k, double n, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the complete elliptic integral \Pi(k,n) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition