Irregular Modified Spherical Bessel Functions

The irregular modified spherical Bessel functions @math{k_l(x)} are related to the irregular modified Bessel functions of fractional order, @math{k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x)}.

Function: double gsl_sf_bessel_k0_scaled (double x)

Function: int gsl_sf_bessel_k0_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled irregular modified spherical Bessel function of zeroth order, @math{\exp(x) k_0(x)}, for @math{x>0}.

Function: double gsl_sf_bessel_k1_scaled (double x)

Function: int gsl_sf_bessel_k1_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled irregular modified spherical Bessel function of first order, @math{\exp(x) k_1(x)}, for @math{x>0}.

Function: double gsl_sf_bessel_k2_scaled (double x)

Function: int gsl_sf_bessel_k2_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled irregular modified spherical Bessel function of second order, @math{\exp(x) k_2(x)}, for @math{x>0}.

Function: double gsl_sf_bessel_kl_scaled (int l, double x)

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

These routines compute the scaled irregular modified spherical Bessel function of order l, @math{\exp(x) k_l(x)}, for @math{x>0}.

Function: int gsl_sf_bessel_kl_scaled_array (int lmax, double x, double result_array[])

This routine computes the values of the scaled irregular modified spherical Bessel functions @math{\exp(x) k_l(x)} for @math{l} from 0 to lmax inclusive for @c{$lmax \geq 0$} @math{lmax >= 0} and @math{x>0}, storing the results in the array result_array. The values are computed using recurrence relations, for efficiency, and therefore may differ slightly from the exact values.