GNU Scientific Library – Reference Manual: Conical Functions

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#### 7.24.3 Conical Functions

The Conical Functions P^\mu_{-(1/2)+i\lambda}(x) and 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 P^{1/2}_{-1/2 + i \lambda}(x) for 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 P^{-1/2}_{-1/2 + i \lambda}(x) for 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 P^0_{-1/2 + i \lambda}(x) for 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 P^1_{-1/2 + i \lambda}(x) for 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 P^{-1/2-l}_{-1/2 + i \lambda}(x) for x > -1, 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 P^{-m}_{-1/2 + i \lambda}(x) for x > -1, m >= -1.