Conical Functions

The Conical Functions @c{$P^\mu_{-(1/2)+i\lambda}(x)$} @math{P^\mu_{-(1/2)+i\lambda}(x)}, @c{$Q^\mu_{-(1/2)+i\lambda}$} @math{Q^\mu_{-(1/2)+i\lambda}} are described in Abramowitz & Stegun, Section 8.12.

Function: double gsl_sf_conicalP_half (double lambda, double x)

Function: int gsl_sf_conicalP_half_e (double lambda, double x, gsl_sf_result * result)

These routines compute the irregular Spherical Conical Function @math{P^{1/2}_{-1/2 + i \lambda}(x)} for @math{x > -1}.

Function: double gsl_sf_conicalP_mhalf (double lambda, double x)

Function: int gsl_sf_conicalP_mhalf_e (double lambda, double x, gsl_sf_result * result)

These routines compute the regular Spherical Conical Function @math{P^{-1/2}_{-1/2 + i \lambda}(x)} for @math{x > -1}.

Function: double gsl_sf_conicalP_0 (double lambda, double x)

Function: int gsl_sf_conicalP_0_e (double lambda, double x, gsl_sf_result * result)

These routines compute the conical function @math{P^0_{-1/2 + i \lambda}(x)} for @math{x > -1}.

Function: double gsl_sf_conicalP_1 (double lambda, double x)

Function: int gsl_sf_conicalP_1_e (double lambda, double x, gsl_sf_result * result)

These routines compute the conical function @math{P^1_{-1/2 + i \lambda}(x)} for @math{x > -1}.

Function: double gsl_sf_conicalP_sph_reg (int l, double lambda, double x)

Function: int gsl_sf_conicalP_sph_reg_e (int l, double lambda, double x, gsl_sf_result * result)

These routines compute the Regular Spherical Conical Function @math{P^{-1/2-l}_{-1/2 + i \lambda}(x)} for @math{x > -1}, @c{$l \ge -1$} @math{l >= -1}.

Function: double gsl_sf_conicalP_cyl_reg (int m, double lambda, double x)

Function: int gsl_sf_conicalP_cyl_reg_e (int m, double lambda, double x, gsl_sf_result * result)

These routines compute the Regular Cylindrical Conical Function @math{P^{-m}_{-1/2 + i \lambda}(x)} for @math{x > -1}, @c{$m \ge -1$} @math{m >= -1}.