#### 7.5.8 Irregular Modified Spherical Bessel Functions

The irregular modified spherical Bessel functions k_l(x) are related to the irregular modified Bessel functions of fractional order, 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, \exp(x) k_0(x), for 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, \exp(x) k_1(x), for 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, \exp(x) k_2(x), for 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, \exp(x) k_l(x), for 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 \exp(x) k_l(x) for l from 0 to lmax inclusive for lmax >= 0 and 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.

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