Conical Functions
The Conical Functions
P^\mu_{-(1/2)+i\lambda}(x),
Q^\mu_{-(1/2)+i\lambda}
are described in Abramowitz & Stegun, Section 8.12.
- Function: double gsl_sf_conicalP_half (double lambda, double x)
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- Function: int gsl_sf_conicalP_half_e (double lambda, double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_conicalP_mhalf_e (double lambda, double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_conicalP_0_e (double lambda, double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_conicalP_1_e (double lambda, double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_conicalP_sph_reg_e (int l, double lambda, double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_conicalP_cyl_reg_e (int m, double lambda, double x, gsl_sf_result * result)
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These routines compute the Regular Cylindrical Conical Function
P^{-m}_{-1/2 + i \lambda}(x) for x > -1,
m >= -1.