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
.
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
.
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 P(\phi,k,n) to the accuracy specified by the mode variable
mode
.
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,n) which is defined through the Carlson form RD(x,y,z) by the following relation,
D(\phi,k,n) = RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).