#### 7.5.3 Regular Modified Cylindrical Bessel Functions

— Function: double gsl_sf_bessel_I0 (double x)
— Function: int gsl_sf_bessel_I0_e (double x, gsl_sf_result * result)

These routines compute the regular modified cylindrical Bessel function of zeroth order, I_0(x).

— Function: double gsl_sf_bessel_I1 (double x)
— Function: int gsl_sf_bessel_I1_e (double x, gsl_sf_result * result)

These routines compute the regular modified cylindrical Bessel function of first order, I_1(x).

— Function: double gsl_sf_bessel_In (int n, double x)
— Function: int gsl_sf_bessel_In_e (int n, double x, gsl_sf_result * result)

These routines compute the regular modified cylindrical Bessel function of order n, I_n(x).

— Function: int gsl_sf_bessel_In_array (int nmin, int nmax, double x, double result_array[])

This routine computes the values of the regular modified cylindrical Bessel functions I_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.

— 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 cylindrical 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 cylindrical Bessel function of first order \exp(-|x|) I_1(x).

— Function: double gsl_sf_bessel_In_scaled (int n, double x)
— Function: int gsl_sf_bessel_In_scaled_e (int n, double x, gsl_sf_result * result)

These routines compute the scaled regular modified cylindrical Bessel function of order n, \exp(-|x|) I_n(x)

— Function: int gsl_sf_bessel_In_scaled_array (int nmin, int nmax, double x, double result_array[])

This routine computes the values of the scaled regular cylindrical Bessel functions \exp(-|x|) I_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.

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