Irregular Modified Cylindrical Bessel Functions

Function: double gsl_sf_bessel_K0 (double x)

Function: int gsl_sf_bessel_K0_e (double x, gsl_sf_result * result)

These routines compute the irregular modified cylindrical Bessel function of zeroth order, @math{K_0(x)}, for @math{x > 0}.

Function: double gsl_sf_bessel_K1 (double x)

Function: int gsl_sf_bessel_K1_e (double x, gsl_sf_result * result)

These routines compute the irregular modified cylindrical Bessel function of first order, @math{K_1(x)}, for @math{x > 0}.

Function: double gsl_sf_bessel_Kn (int n, double x)

Function: int gsl_sf_bessel_Kn_e (int n, double x, gsl_sf_result * result)

These routines compute the irregular modified cylindrical Bessel function of order n, @math{K_n(x)}, for @math{x > 0}.

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

This routine computes the values of the irregular modified cylindrical Bessel functions @math{K_n(x)} for @math{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 domain of the function is @math{x>0}. The values are computed using recurrence relations, for efficiency, and therefore may differ slightly from the exact values.

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 cylindrical 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 cylindrical Bessel function of first order @math{\exp(x) K_1(x)} for @math{x>0}.

Function: double gsl_sf_bessel_Kn_scaled (int n, double x)

Function: int gsl_sf_bessel_Kn_scaled_e (int n, double x, gsl_sf_result * result)

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

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

This routine computes the values of the scaled irregular cylindrical Bessel functions @math{\exp(x) K_n(x)} for @math{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 domain of the function is @math{x>0}. The values are computed using recurrence relations, for efficiency, and therefore may differ slightly from the exact values.