Regular Modified Spherical Bessel Functions

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

Function: double gsl_sf_bessel_i0_scaled (double x)

Function: int gsl_sf_bessel_i0_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled regular modified spherical Bessel function of zeroth order, @math{\exp(-|x|) i_0(x)}.

Function: double gsl_sf_bessel_i1_scaled (double x)

Function: int gsl_sf_bessel_i1_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled regular modified spherical Bessel function of first order, @math{\exp(-|x|) i_1(x)}.

Function: double gsl_sf_bessel_i2_scaled (double x)

Function: int gsl_sf_bessel_i2_scaled_e (double x, gsl_sf_result * result)

These routines compute the scaled regular modified spherical Bessel function of second order, @math{ \exp(-|x|) i_2(x) }

Function: double gsl_sf_bessel_il_scaled (int l, double x)

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

These routines compute the scaled regular modified spherical Bessel function of order l, @math{ \exp(-|x|) i_l(x) }

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

This routine computes the values of the scaled regular modified cylindrical Bessel functions @math{\exp(-|x|) i_l(x)} for @math{l} from 0 to lmax inclusive for @c{$lmax \geq 0$} @math{lmax >= 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.