Regular Spherical Bessel Functions
- Function: double gsl_sf_bessel_j0 (double x)
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- Function: int gsl_sf_bessel_j0_e (double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_bessel_j1_e (double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_bessel_j2_e (double x, gsl_sf_result * result)
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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)
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- Function: int gsl_sf_bessel_jl_e (int l, double x, gsl_sf_result * result)
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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[])
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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)
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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.