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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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7.5.5 Regular Spherical Bessel Functions

Function: double gsl_sf_bessel_j0 (double x)
Function: int gsl_sf_bessel_j0_e (double x, gsl_sf_result * result)
These routines compute the regular spherical Bessel function of zeroth order, j_0(x) = \sin(x)/x.
Function: double gsl_sf_bessel_j1 (double x)
Function: int gsl_sf_bessel_j1_e (double x, gsl_sf_result * result)
These routines compute the regular spherical Bessel function of first order, j_1(x) = (\sin(x)/x - \cos(x))/x.
Function: double gsl_sf_bessel_j2 (double x)
Function: int gsl_sf_bessel_j2_e (double x, gsl_sf_result * result)
These routines compute the regular spherical Bessel function of second order, j_2(x) = ((3/x^2 - 1)\sin(x) - 3\cos(x)/x)/x.
Function: double gsl_sf_bessel_jl (int l, double x)
Function: int gsl_sf_bessel_jl_e (int l, double x, gsl_sf_result * result)
These routines compute the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0.
Function: int gsl_sf_bessel_jl_array (int lmax, double x, double result_array[])
This routine computes the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 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.
Function: int gsl_sf_bessel_jl_steed_array (int lmax, double x, double * jl_x_array)
This routine uses Steed's method to compute the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 0, storing the results in the array result_array. The Steed/Barnett algorithm is described in Comp. Phys. Comm. 21, 297 (1981). Steed's method is more stable than the recurrence used in the other functions but is also slower.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition