GNU Scientific Library – Reference Manual: Irregular Spherical Bessel Functions

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#### 7.5.6 Irregular Spherical Bessel Functions

Function: double gsl_sf_bessel_y0 (double x)
Function: int gsl_sf_bessel_y0_e (double x, gsl_sf_result * result)

  These routines compute the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x.

Function: double gsl_sf_bessel_y1 (double x)
Function: int gsl_sf_bessel_y1_e (double x, gsl_sf_result * result)

  These routines compute the irregular spherical Bessel function of first order, y_1(x) = -(\cos(x)/x + \sin(x))/x.

Function: double gsl_sf_bessel_y2 (double x)
Function: int gsl_sf_bessel_y2_e (double x, gsl_sf_result * result)

  These routines compute the irregular spherical Bessel function of second order, y_2(x) = (-3/x^3 + 1/x)\cos(x) - (3/x^2)\sin(x).

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

  These routines compute the irregular spherical Bessel function of order l, y_l(x), for l >= 0.

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

  This routine computes the values of the irregular spherical Bessel functions y_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.