GNU Scientific Library – Reference Manual: Regular Modified Spherical Bessel Functions

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#### 7.5.7 Regular Modified Spherical Bessel Functions

The regular modified spherical Bessel functions i_l(x) are related to the modified Bessel functions of fractional order, 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, \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, \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, \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, \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 \exp(-|x|) i_l(x) for l from 0 to lmax inclusive for 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.