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

package info (click to toggle)
gsl-ref-html 2.3-1
• area: non-free
• in suites: bullseye, buster, sid
• size: 6,876 kB
• ctags: 4,574
• sloc: makefile: 35
 file content (119 lines) | stat: -rw-r--r-- 6,878 bytes parent folder | download
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119  GNU Scientific Library – Reference Manual: Legendre Form of Incomplete Elliptic Integrals

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, gsl_mode_t mode)
Function: int gsl_sf_ellint_D_e (double phi, double k, 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) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).