Legendre Form of Complete Elliptic Integrals - GNU Scientific Library -- Reference Manual

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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.

— 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.