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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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7.13.4 Legendre Form of Incomplete Elliptic Integrals

Function: double gsl_sf_ellint_F (double phi, double k, gsl_mode_t mode)
Function: int gsl_sf_ellint_F_e (double phi, double k, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the incomplete elliptic integral F(\phi,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_E (double phi, double k, gsl_mode_t mode)
Function: int gsl_sf_ellint_E_e (double phi, double k, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the incomplete elliptic integral E(\phi,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_P (double phi, double k, double n, gsl_mode_t mode)
Function: int gsl_sf_ellint_P_e (double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result)
These routines compute the incomplete elliptic integral \Pi(\phi,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.
Function: double gsl_sf_ellint_D (double phi, double k, double n, gsl_mode_t mode)
Function: int gsl_sf_ellint_D_e (double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result)
These functions compute the incomplete elliptic integral D(\phi,k) which is defined through the Carlson form RD(x,y,z) by the following relation,
D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).

The argument n is not used and will be removed in a future release.

ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition