## File: Legendre-Form-of-Complete-Elliptic-Integrals.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105  GNU Scientific Library – Reference Manual: Legendre Form of Complete Elliptic Integrals

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.