- publishing free software manuals
 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. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

### 7.5.7 Regular Modified Spherical Bessel Functions

The regular modified spherical Bessel functions i_l(x) are related to the modified Bessel functions of fractional order, i_l(x) = \sqrt{\pi/(2x)} I_{l+1/2}(x)

Function: double gsl_sf_bessel_i0_scaled (double x)
Function: int gsl_sf_bessel_i0_scaled_e (double x, gsl_sf_result * result)
These routines compute the scaled regular modified spherical Bessel function of zeroth order, \exp(-|x|) i_0(x).
Function: double gsl_sf_bessel_i1_scaled (double x)
Function: int gsl_sf_bessel_i1_scaled_e (double x, gsl_sf_result * result)
These routines compute the scaled regular modified spherical Bessel function of first order, \exp(-|x|) i_1(x).
Function: double gsl_sf_bessel_i2_scaled (double x)
Function: int gsl_sf_bessel_i2_scaled_e (double x, gsl_sf_result * result)
These routines compute the scaled regular modified spherical Bessel function of second order, \exp(-|x|) i_2(x)
Function: double gsl_sf_bessel_il_scaled (int l, double x)
Function: int gsl_sf_bessel_il_scaled_e (int l, double x, gsl_sf_result * result)
These routines compute the scaled regular modified spherical Bessel function of order l, \exp(-|x|) i_l(x)
Function: int gsl_sf_bessel_il_scaled_array (int lmax, double x, double result_array[])
This routine computes the values of the scaled regular modified cylindrical Bessel functions \exp(-|x|) i_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.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition