#### 7.5.4 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, K_0(x), for 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, K_1(x), for 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, K_n(x), for 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 K_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 domain of the function is 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 \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 cylindrical Bessel function of first order \exp(x) K_1(x) for 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, \exp(x) K_n(x), for 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 \exp(x) K_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 domain of the function is x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.