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.\" ========================================================================
.\"
.IX Title "Math::GSL::SF 3pm"
.TH Math::GSL::SF 3pm "2019-02-23" "perl v5.28.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::GSL::SF \- Special Functions
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&    use Math::GSL::SF qw/:all/;
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module contains a data structure named gsl_sf_result. To create a new one use
.PP
.Vb 1
\&    $r = Math::GSL::SF::gsl_sf_result_struct\->new;
.Ve
.PP
You can then access the elements of the structure in this way :
.PP
.Vb 1
\&    my $val   = $r\->{val};
\&
\&    my $error = $r\->{err};
.Ve
.PP
Here is a list of all included functions:
.ie n .IP """gsl_sf_airy_Ai_e($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_e($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Ai_e($x, $mode)"
.PD 0
.ie n .IP """gsl_sf_airy_Ai($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Ai($x, $mode, $result)"
.PD
.Vb 1
\& These routines compute the Airy function Ai($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_airy_Bi_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Bi_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Bi($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Bi($x, $mode)"
.PD
.Vb 1
\& These routines compute the Airy function Bi($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_airy_Ai_scaled_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_scaled_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Ai_scaled_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Ai_scaled($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_scaled($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Ai_scaled($x, $mode)"
.PD
.Vb 1
\& These routines compute a scaled version of the Airy function S_A($x) Ai($x). For $x>0 the scaling factor S_A($x) is \eexp(+(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_airy_Bi_scaled_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_scaled_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Bi_scaled_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Bi_scaled($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_scaled($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Bi_scaled($x, $mode)"
.PD
.Vb 1
\& These routines compute a scaled version of the Airy function S_B($x) Bi($x). For $x>0 the scaling factor S_B($x) is exp(\-(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_airy_Ai_deriv_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_deriv_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Ai_deriv_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Ai_deriv($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_deriv($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Ai_deriv($x, $mode)"
.PD
.Vb 1
\& These routines compute the Airy function derivative Ai\*(Aq($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_airy_Bi_deriv_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_deriv_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Bi_deriv_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Bi_deriv($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_deriv($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Bi_deriv($x, $mode)"
.PD
These routines compute the Airy function derivative Bi'($x) with an accuracy specified by \f(CW$mode\fR. \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Ai_deriv_scaled($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Ai_deriv_scaled($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Ai_deriv_scaled($x, $mode)"
.PD
These routines compute the scaled Airy function derivative S_A(x) Ai'(x). For x>0 the scaling factor S_A(x) is \eexp(+(2/3) x^(3/2)), and is 1 for x<0. \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)\fR" 4
.IX Item "gsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_Bi_deriv_scaled($x, $mode)""" 4
.el .IP "\f(CWgsl_sf_airy_Bi_deriv_scaled($x, $mode)\fR" 4
.IX Item "gsl_sf_airy_Bi_deriv_scaled($x, $mode)"
.PD
These routines compute the scaled Airy function derivative S_B(x) Bi'(x). For x>0 the scaling factor S_B(x) is exp(\-(2/3) x^(3/2)), and is 1 for x<0. \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_zero_Ai_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Ai_e($s, $result)\fR" 4
.IX Item "gsl_sf_airy_zero_Ai_e($s, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_zero_Ai($s)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Ai($s)\fR" 4
.IX Item "gsl_sf_airy_zero_Ai($s)"
.PD
These routines compute the location of the s\-th zero of the Airy function Ai($x). \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_zero_Bi_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Bi_e($s, $result)\fR" 4
.IX Item "gsl_sf_airy_zero_Bi_e($s, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_zero_Bi($s)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Bi($s)\fR" 4
.IX Item "gsl_sf_airy_zero_Bi($s)"
.PD
These routines compute the location of the s\-th zero of the Airy function Bi($x). \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_zero_Ai_deriv_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Ai_deriv_e($s, $result)\fR" 4
.IX Item "gsl_sf_airy_zero_Ai_deriv_e($s, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_zero_Ai_deriv($s)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Ai_deriv($s)\fR" 4
.IX Item "gsl_sf_airy_zero_Ai_deriv($s)"
.PD
These routines compute the location of the s\-th zero of the Airy function derivative Ai'(x). \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_airy_zero_Bi_deriv_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Bi_deriv_e($s, $result)\fR" 4
.IX Item "gsl_sf_airy_zero_Bi_deriv_e($s, $result)"
.PD 0
.ie n .IP """gsl_sf_airy_zero_Bi_deriv($s)""" 4
.el .IP "\f(CWgsl_sf_airy_zero_Bi_deriv($s)\fR" 4
.IX Item "gsl_sf_airy_zero_Bi_deriv($s)"
.PD
.Vb 1
\& These routines compute the location of the s\-th zero of the Airy function derivative Bi\*(Aq(x). $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_bessel_J0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_J0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_J0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_J0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_J0($x)\fR" 4
.IX Item "gsl_sf_bessel_J0($x)"
.PD
These routines compute the regular cylindrical Bessel function of zeroth order, J_0($x). \f(CW$result\fR is a gsl_sf_result structure.
.ie n .IP """gsl_sf_bessel_J1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_J1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_J1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_J1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_J1($x)\fR" 4
.IX Item "gsl_sf_bessel_J1($x)"
.PD
.Vb 1
\& These routines compute the regular cylindrical Bessel function of first order, J_1($x). $result is a gsl_sf_result structure.
.Ve
.ie n .IP """gsl_sf_bessel_Jn_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Jn_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Jn_e($n, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Jn($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Jn($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_Jn($n, $x)"
.PD
These routines compute the regular cylindrical Bessel function of order n, J_n($x).
.ie n .IP """gsl_sf_bessel_Jn_array($nmin, $nmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Jn_array($nmin, $nmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_Jn_array($nmin, $nmax, $x)"
This routine computes the values of the regular cylindrical Bessel functions
J_n($x) for n from \f(CW$nmin\fR to \f(CW$nmax\fR inclusive, returning the results in an array
reference. The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
.ie n .IP """gsl_sf_bessel_Y0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Y0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Y0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Y0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Y0($x)\fR" 4
.IX Item "gsl_sf_bessel_Y0($x)"
.PD
.Vb 1
\& These routines compute the irregular spherical Bessel function of zeroth order, y_0(x) = \-\ecos(x)/x.
.Ve
.ie n .IP """gsl_sf_bessel_Y1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Y1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Y1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Y1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Y1($x)\fR" 4
.IX Item "gsl_sf_bessel_Y1($x)"
.PD
These routines compute the irregular spherical Bessel function of first order, y_1(x) = \-(\ecos(x)/x + \esin(x))/x.
.ie n .IP """gsl_sf_bessel_Yn_e""($n, $x, $result)" 4
.el .IP "\f(CWgsl_sf_bessel_Yn_e\fR($n, \f(CW$x\fR, \f(CW$result\fR)" 4
.IX Item "gsl_sf_bessel_Yn_e($n, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Yn($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Yn($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_Yn($n, $x)"
.PD
These routines compute the irregular cylindrical Bessel function of order \f(CW$n\fR, Y_n(x), for x>0.
.ie n .IP """gsl_sf_bessel_Yn_array($nmin, $nmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Yn_array($nmin, $nmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_Yn_array($nmin, $nmax, $x)"
This routine computes the values of the irregular cylindrical Bessel functions
Y_n(x) for n from \f(CW$nmin\fR to \f(CW$nmax\fR inclusive, returning the results in an array
reference. The domain of the function is \f(CW$x\fR>0. The values are computed using
recurrence relations for efficiency, and therefore may differ slightly from the
exact values.
.ie n .IP """gsl_sf_bessel_I0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_I0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_I0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_I0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_I0($x)\fR" 4
.IX Item "gsl_sf_bessel_I0($x)"
.PD
These routines compute the regular modified cylindrical Bessel function of zeroth order, I_0(x).
.ie n .IP """gsl_sf_bessel_I1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_I1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_I1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_I1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_I1($x)\fR" 4
.IX Item "gsl_sf_bessel_I1($x)"
.ie n .IP """gsl_sf_bessel_In_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_In_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_In_e($n, $x, $result)"
.ie n .IP """gsl_sf_bessel_In($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_In($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_In($n, $x)"
.PD
These routines compute the regular modified cylindrical Bessel function of order \f(CW$n\fR, I_n(x).
.ie n .IP """gsl_sf_bessel_In_array($nmin, $nmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_In_array($nmin, $nmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_In_array($nmin, $nmax, $x)"
This routine computes the values of the regular modified cylindrical Bessel
functions I_n(x) for n from \f(CW$nmin\fR to \f(CW$nmax\fR inclusive, returning the results in an
array reference. The start of the range nmin must be positive or zero. The
values are computed using recurrence relations for efficiency, and therefore may
differ slightly from the exact values.
.ie n .IP """gsl_sf_bessel_I0_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_I0_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_I0_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_I0_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_I0_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_I0_scaled($x)"
.PD
These routines compute the scaled regular modified cylindrical Bessel function of zeroth order \eexp(\-|x|) I_0(x).
.ie n .IP """gsl_sf_bessel_I1_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_I1_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_I1_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_I1_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_I1_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_I1_scaled($x)"
.PD
These routines compute the scaled regular modified cylindrical Bessel function of first order \eexp(\-|x|) I_1(x).
.ie n .IP """gsl_sf_bessel_In_scaled_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_In_scaled_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_In_scaled_e($n, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_In_scaled($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_In_scaled($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_In_scaled($n, $x)"
.PD
These routines compute the scaled regular modified cylindrical Bessel function of order \f(CW$n\fR, \eexp(\-|x|) I_n(x)
.ie n .IP """gsl_sf_bessel_In_scaled_array($nmin, $nmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_In_scaled_array($nmin, $nmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_In_scaled_array($nmin, $nmax, $x)"
This routine computes the values of the scaled regular cylindrical Bessel
functions exp(\-|$x|) I_n($x) for n from \f(CW$nmin\fR to \f(CW$nmax\fR inclusive, returning the
results in an array reference. The start of the range nmin must be positive
or zero. The values are computed using recurrence relations for efficiency, and
therefore may differ slightly from the exact values.
.ie n .IP """gsl_sf_bessel_K0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_K0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_K0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_K0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_K0($x)\fR" 4
.IX Item "gsl_sf_bessel_K0($x)"
.PD
These routines compute the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0.
.ie n .IP """gsl_sf_bessel_K1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_K1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_K1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_K1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_K1($x)\fR" 4
.IX Item "gsl_sf_bessel_K1($x)"
.PD
These routines compute the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0.
.ie n .IP """gsl_sf_bessel_Kn_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Kn_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Kn_e($n, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Kn($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Kn($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_Kn($n, $x)"
.PD
These routines compute the irregular modified cylindrical Bessel function of order \f(CW$n\fR, K_n(x), for x > 0.
.ie n .IP """gsl_sf_bessel_Kn_array($nmin, $nmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Kn_array($nmin, $nmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_Kn_array($nmin, $nmax, $x)"
This routine computes the values of the Irregular Modified Cylindrical Bessel Functions
K_n($x) for n from \f(CW$nmin\fR to \f(CW$nmax\fR inclusive, returning the results in an array
reference. The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
This function is only defined for positive \f(CW$x\fR and with throw an exception otherwise.
.ie n .IP """gsl_sf_bessel_K0_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_K0_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_K0_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_K0_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_K0_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_K0_scaled($x)"
.PD
These routines compute the scaled irregular modified cylindrical Bessel function of zeroth order \eexp(x) K_0(x) for x>0.
.ie n .IP """gsl_sf_bessel_K1_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_K1_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_K1_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_K1_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_K1_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_K1_scaled($x)"
.ie n .IP """gsl_sf_bessel_Kn_scaled_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Kn_scaled_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Kn_scaled_e($n, $x, $result)"
.ie n .IP """gsl_sf_bessel_Kn_scaled($n, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Kn_scaled($n, $x)\fR" 4
.IX Item "gsl_sf_bessel_Kn_scaled($n, $x)"
.ie n .IP """gsl_sf_bessel_Kn_scaled_array($nmin, $max, $x) """ 4
.el .IP "\f(CWgsl_sf_bessel_Kn_scaled_array($nmin, $max, $x) \fR" 4
.IX Item "gsl_sf_bessel_Kn_scaled_array($nmin, $max, $x) "
.PD
This routine computes the values of the scaled irregular cylindrical Bessel
functions exp(x) K_n(x) for n from nmin to nmax inclusive, storing the results
in the array result_array. The start of the range nmin must be positive or zero.
The domain of the function is x>0. The values are computed using recurrence
relations for efficiency, and therefore may differ slightly from the exact
values.
.ie n .IP """gsl_sf_bessel_j0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_j0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_j0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_j0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_j0($x)\fR" 4
.IX Item "gsl_sf_bessel_j0($x)"
.ie n .IP """gsl_sf_bessel_j1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_j1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_j1_e($x, $result)"
.ie n .IP """gsl_sf_bessel_j1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_j1($x)\fR" 4
.IX Item "gsl_sf_bessel_j1($x)"
.ie n .IP """gsl_sf_bessel_j2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_j2_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_j2_e($x, $result)"
.ie n .IP """gsl_sf_bessel_j2($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_j2($x)\fR" 4
.IX Item "gsl_sf_bessel_j2($x)"
.ie n .IP """gsl_sf_bessel_jl_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_jl_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_jl_e($l, $x, $result)"
.ie n .IP """gsl_sf_bessel_jl($l, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_jl($l, $x)\fR" 4
.IX Item "gsl_sf_bessel_jl($l, $x)"
.ie n .IP """gsl_sf_bessel_jl_array($lmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_jl_array($lmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_jl_array($lmax, $x)"
.PD
This routine computes the values of the regular spherical Bessel functions
j_l(x) for l from 0 to \f(CW$lmax\fR inclusive for \f(CW$lmax\fR >= 0 and \f(CW$x\fR >= 0, returning
the results in an array reference. The values are computed using recurrence
relations for efficiency, and therefore may differ slightly from the exact
values.
.ie n .IP """gsl_sf_bessel_jl_steed_array($lmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_jl_steed_array($lmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_jl_steed_array($lmax, $x)"
This routine uses SteedXs method to compute the values of the regular spherical
Bessel functions j_l(x) for l from 0 to \f(CW$lmax\fR inclusive for \f(CW$lmax\fR >= 0 and \f(CW$x\fR >= 0,
storing the results in the array result_array. The Steed/Barnett algorithm is
described in Comp. Phys. Comm. 21, 297 (1981). SteedXs method is more stable
than the recurrence used in the other functions but is also slower.
.ie n .IP """gsl_sf_bessel_y0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_y0_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_y0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_y0($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_y0($x)\fR" 4
.IX Item "gsl_sf_bessel_y0($x)"
.ie n .IP """gsl_sf_bessel_y1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_y1_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_y1_e($x, $result)"
.ie n .IP """gsl_sf_bessel_y1($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_y1($x)\fR" 4
.IX Item "gsl_sf_bessel_y1($x)"
.ie n .IP """gsl_sf_bessel_y2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_y2_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_y2_e($x, $result)"
.ie n .IP """gsl_sf_bessel_y2($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_y2($x)\fR" 4
.IX Item "gsl_sf_bessel_y2($x)"
.ie n .IP """gsl_sf_bessel_yl_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_yl_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_yl_e($l, $x, $result)"
.ie n .IP """gsl_sf_bessel_yl($l, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_yl($l, $x)\fR" 4
.IX Item "gsl_sf_bessel_yl($l, $x)"
.ie n .IP """gsl_sf_bessel_yl_array($lmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_yl_array($lmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_yl_array($lmax, $x)"
.PD
This routine computes the values of the irregular spherical Bessel functions
y_l(x) for l from 0 to \f(CW$lmax\fR inclusive for lmax >= 0, returning the results in an
array reference. The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
.ie n .IP """gsl_sf_bessel_i0_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_i0_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_i0_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_i0_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_i0_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_i0_scaled($x)"
.ie n .IP """gsl_sf_bessel_i1_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_i1_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_i1_scaled_e($x, $result)"
.ie n .IP """gsl_sf_bessel_i1_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_i1_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_i1_scaled($x)"
.ie n .IP """gsl_sf_bessel_i2_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_i2_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_i2_scaled_e($x, $result)"
.ie n .IP """gsl_sf_bessel_i2_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_i2_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_i2_scaled($x)"
.ie n .IP """gsl_sf_bessel_il_scaled_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_il_scaled_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_il_scaled_e($l, $x, $result)"
.ie n .IP """gsl_sf_bessel_il_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_il_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_il_scaled($x)"
.ie n .IP """gsl_sf_bessel_il_scaled_array($lmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_il_scaled_array($lmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_il_scaled_array($lmax, $x)"
.PD
This routine computes the values of the scaled regular modified spherical Bessel
functions exp(\-|x|) i_l(x) for l from 0 to \f(CW$lmax\fR inclusive for \f(CW$lmax\fR >= 0,
returning the results in an array reference. The values are computed using
recurrence relations for efficiency, and therefore may differ slightly from the
exact values.
.ie n .IP """gsl_sf_bessel_k0_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_k0_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_k0_scaled_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_k0_scale($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_k0_scale($x)\fR" 4
.IX Item "gsl_sf_bessel_k0_scale($x)"
.ie n .IP """gsl_sf_bessel_k1_scaled_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_k1_scaled_e($x, $result)\fR" 4
.IX Item "gsl_sf_bessel_k1_scaled_e($x, $result)"
.ie n .IP """gsl_sf_bessel_k1_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_k1_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_k1_scaled($x)"
.ie n .IP """gsl_sf_bessel_k2_scaled_e($x, $result) """ 4
.el .IP "\f(CWgsl_sf_bessel_k2_scaled_e($x, $result) \fR" 4
.IX Item "gsl_sf_bessel_k2_scaled_e($x, $result) "
.ie n .IP """gsl_sf_bessel_k2_scaled($x)""" 4
.el .IP "\f(CWgsl_sf_bessel_k2_scaled($x)\fR" 4
.IX Item "gsl_sf_bessel_k2_scaled($x)"
.ie n .IP """gsl_sf_bessel_kl_scaled_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_kl_scaled_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_kl_scaled_e($l, $x, $result)"
.ie n .IP """gsl_sf_bessel_kl_scaled($l, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_kl_scaled($l, $x)\fR" 4
.IX Item "gsl_sf_bessel_kl_scaled($l, $x)"
.ie n .IP """gsl_sf_bessel_kl_scaled_array($lmax, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_kl_scaled_array($lmax, $x)\fR" 4
.IX Item "gsl_sf_bessel_kl_scaled_array($lmax, $x)"
.PD
This routine computes the values of the scaled irregular modified spherical Bessel
functions exp($x) k_l($x) for l from 0 to lmax inclusive for \f(CW$lmax\fR >= 0 and \f(CW$x\fR>0,
returning the results in an array reference. The values are computed using
recurrence relations for efficiency, and therefore may differ slightly from the
exact values.
.ie n .IP """gsl_sf_bessel_Jnu_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Jnu_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Jnu_e($nu, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_bessel_Jnu($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Jnu($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Jnu($nu, $x)"
.ie n .IP """gsl_sf_bessel_sequence_Jnu_e """ 4
.el .IP "\f(CWgsl_sf_bessel_sequence_Jnu_e \fR" 4
.IX Item "gsl_sf_bessel_sequence_Jnu_e "
.ie n .IP """gsl_sf_bessel_Ynu_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Ynu_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Ynu_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_Ynu($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Ynu($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Ynu($nu, $x)"
.ie n .IP """gsl_sf_bessel_Inu_scaled_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Inu_scaled_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Inu_scaled_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_Inu_scaled($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Inu_scaled($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Inu_scaled($nu, $x)"
.ie n .IP """gsl_sf_bessel_Inu_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Inu_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Inu_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_Inu($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Inu($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Inu($nu, $x)"
.ie n .IP """gsl_sf_bessel_Knu_scaled_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Knu_scaled_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Knu_scaled_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_Knu_scaled($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Knu_scaled($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Knu_scaled($nu, $x)"
.ie n .IP """gsl_sf_bessel_Knu_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_Knu_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_Knu_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_Knu($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_Knu($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_Knu($nu, $x)"
.ie n .IP """gsl_sf_bessel_lnKnu_e($nu, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_lnKnu_e($nu, $x, $result)\fR" 4
.IX Item "gsl_sf_bessel_lnKnu_e($nu, $x, $result)"
.ie n .IP """gsl_sf_bessel_lnKnu($nu, $x)""" 4
.el .IP "\f(CWgsl_sf_bessel_lnKnu($nu, $x)\fR" 4
.IX Item "gsl_sf_bessel_lnKnu($nu, $x)"
.ie n .IP """gsl_sf_bessel_zero_J0_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_J0_e($s, $result)\fR" 4
.IX Item "gsl_sf_bessel_zero_J0_e($s, $result)"
.ie n .IP """gsl_sf_bessel_zero_J0($s)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_J0($s)\fR" 4
.IX Item "gsl_sf_bessel_zero_J0($s)"
.ie n .IP """gsl_sf_bessel_zero_J1_e($s, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_J1_e($s, $result)\fR" 4
.IX Item "gsl_sf_bessel_zero_J1_e($s, $result)"
.ie n .IP """gsl_sf_bessel_zero_J1($s)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_J1($s)\fR" 4
.IX Item "gsl_sf_bessel_zero_J1($s)"
.ie n .IP """gsl_sf_bessel_zero_Jnu_e($nu, $s, $result)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_Jnu_e($nu, $s, $result)\fR" 4
.IX Item "gsl_sf_bessel_zero_Jnu_e($nu, $s, $result)"
.ie n .IP """gsl_sf_bessel_zero_Jnu($nu, $s)""" 4
.el .IP "\f(CWgsl_sf_bessel_zero_Jnu($nu, $s)\fR" 4
.IX Item "gsl_sf_bessel_zero_Jnu($nu, $s)"
.ie n .IP """gsl_sf_clausen_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_clausen_e($x, $result)\fR" 4
.IX Item "gsl_sf_clausen_e($x, $result)"
.ie n .IP """gsl_sf_clausen($x)""" 4
.el .IP "\f(CWgsl_sf_clausen($x)\fR" 4
.IX Item "gsl_sf_clausen($x)"
.ie n .IP """gsl_sf_hydrogenicR_1_e($Z, $r, $result)""" 4
.el .IP "\f(CWgsl_sf_hydrogenicR_1_e($Z, $r, $result)\fR" 4
.IX Item "gsl_sf_hydrogenicR_1_e($Z, $r, $result)"
.ie n .IP """gsl_sf_hydrogenicR_1($Z, $r)""" 4
.el .IP "\f(CWgsl_sf_hydrogenicR_1($Z, $r)\fR" 4
.IX Item "gsl_sf_hydrogenicR_1($Z, $r)"
.ie n .IP """gsl_sf_hydrogenicR_e($n, $l, $Z, $r, $result)""" 4
.el .IP "\f(CWgsl_sf_hydrogenicR_e($n, $l, $Z, $r, $result)\fR" 4
.IX Item "gsl_sf_hydrogenicR_e($n, $l, $Z, $r, $result)"
.ie n .IP """gsl_sf_hydrogenicR($n, $l, $Z, $r)""" 4
.el .IP "\f(CWgsl_sf_hydrogenicR($n, $l, $Z, $r)\fR" 4
.IX Item "gsl_sf_hydrogenicR($n, $l, $Z, $r)"
.ie n .IP """gsl_sf_coulomb_wave_FG_e($eta, $x, $L_F, $k, $F, gsl_sf_result * Fp, gsl_sf_result * G, $Gp)"" \- This function computes the Coulomb wave functions F_L(\eeta,x), G_{L\-k}(\eeta,x) and their derivatives F'_L(\eeta,x), G'_{L\-k}(\eeta,x) with respect to $x. The parameters are restricted to L, L\-k > \-1/2, x > 0 and integer $k. Note that L itself is not restricted to being an integer. The results are stored in the parameters $F, $G for the function values and $Fp, $Gp for the derivative values. $F, $G, $Fp, $Gp are all gsl_result structs. If an overflow occurs, $GSL_EOVRFLW is returned and scaling exponents are returned as second and third values." 4
.el .IP "\f(CWgsl_sf_coulomb_wave_FG_e($eta, $x, $L_F, $k, $F, gsl_sf_result * Fp, gsl_sf_result * G, $Gp)\fR \- This function computes the Coulomb wave functions F_L(\eeta,x), G_{L\-k}(\eeta,x) and their derivatives F'_L(\eeta,x), G'_{L\-k}(\eeta,x) with respect to \f(CW$x\fR. The parameters are restricted to L, L\-k > \-1/2, x > 0 and integer \f(CW$k\fR. Note that L itself is not restricted to being an integer. The results are stored in the parameters \f(CW$F\fR, \f(CW$G\fR for the function values and \f(CW$Fp\fR, \f(CW$Gp\fR for the derivative values. \f(CW$F\fR, \f(CW$G\fR, \f(CW$Fp\fR, \f(CW$Gp\fR are all gsl_result structs. If an overflow occurs, \f(CW$GSL_EOVRFLW\fR is returned and scaling exponents are returned as second and third values." 4
.IX Item "gsl_sf_coulomb_wave_FG_e($eta, $x, $L_F, $k, $F, gsl_sf_result * Fp, gsl_sf_result * G, $Gp) - This function computes the Coulomb wave functions F_L(eta,x), G_{L-k}(eta,x) and their derivatives F'_L(eta,x), G'_{L-k}(eta,x) with respect to $x. The parameters are restricted to L, L-k > -1/2, x > 0 and integer $k. Note that L itself is not restricted to being an integer. The results are stored in the parameters $F, $G for the function values and $Fp, $Gp for the derivative values. $F, $G, $Fp, $Gp are all gsl_result structs. If an overflow occurs, $GSL_EOVRFLW is returned and scaling exponents are returned as second and third values."
.ie n .IP """gsl_sf_coulomb_wave_F_array "" \-" 4
.el .IP "\f(CWgsl_sf_coulomb_wave_F_array \fR \-" 4
.IX Item "gsl_sf_coulomb_wave_F_array -"
.ie n .IP """gsl_sf_coulomb_wave_FG_array"" \-" 4
.el .IP "\f(CWgsl_sf_coulomb_wave_FG_array\fR \-" 4
.IX Item "gsl_sf_coulomb_wave_FG_array -"
.ie n .IP """gsl_sf_coulomb_wave_FGp_array"" \-" 4
.el .IP "\f(CWgsl_sf_coulomb_wave_FGp_array\fR \-" 4
.IX Item "gsl_sf_coulomb_wave_FGp_array -"
.ie n .IP """gsl_sf_coulomb_wave_sphF_array"" \-" 4
.el .IP "\f(CWgsl_sf_coulomb_wave_sphF_array\fR \-" 4
.IX Item "gsl_sf_coulomb_wave_sphF_array -"
.ie n .IP """gsl_sf_coulomb_CL_e($L, $eta, $result)"" \- This function computes the Coulomb wave function normalization constant C_L($eta) for $L > \-1." 4
.el .IP "\f(CWgsl_sf_coulomb_CL_e($L, $eta, $result)\fR \- This function computes the Coulomb wave function normalization constant C_L($eta) for \f(CW$L\fR > \-1." 4
.IX Item "gsl_sf_coulomb_CL_e($L, $eta, $result) - This function computes the Coulomb wave function normalization constant C_L($eta) for $L > -1."
.ie n .IP """gsl_sf_coulomb_CL_arrayi"" \-" 4
.el .IP "\f(CWgsl_sf_coulomb_CL_arrayi\fR \-" 4
.IX Item "gsl_sf_coulomb_CL_arrayi -"
.ie n .IP """gsl_sf_coupling_3j_e($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc, $result)""" 4
.el .IP "\f(CWgsl_sf_coupling_3j_e($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc, $result)\fR" 4
.IX Item "gsl_sf_coupling_3j_e($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc, $result)"
.ie n .IP """gsl_sf_coupling_3j($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc)""" 4
.el .IP "\f(CWgsl_sf_coupling_3j($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc)\fR" 4
.IX Item "gsl_sf_coupling_3j($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc)"
.PD
.Vb 4
\& These routines compute the Wigner 3\-j coefficient,
\&   (ja jb jc
\&    ma mb mc)
\& where the arguments are given in half\-integer units, ja = $two_ja/2, ma = $two_ma/2, etc.
.Ve
.ie n .IP """gsl_sf_coupling_6j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $result)""" 4
.el .IP "\f(CWgsl_sf_coupling_6j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $result)\fR" 4
.IX Item "gsl_sf_coupling_6j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $result)"
.PD 0
.ie n .IP """gsl_sf_coupling_6j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf)""" 4
.el .IP "\f(CWgsl_sf_coupling_6j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf)\fR" 4
.IX Item "gsl_sf_coupling_6j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf)"
.PD
.Vb 4
\& These routines compute the Wigner 6\-j coefficient,
\&   {ja jb jc
\&    jd je jf}
\& where the arguments are given in half\-integer units, ja = $two_ja/2, ma = $two_ma/2, etc.
.Ve
.ie n .IP """gsl_sf_coupling_RacahW_e""" 4
.el .IP "\f(CWgsl_sf_coupling_RacahW_e\fR" 4
.IX Item "gsl_sf_coupling_RacahW_e"
.PD 0
.ie n .IP """gsl_sf_coupling_RacahW""" 4
.el .IP "\f(CWgsl_sf_coupling_RacahW\fR" 4
.IX Item "gsl_sf_coupling_RacahW"
.ie n .IP """gsl_sf_coupling_9j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji, $result)""" 4
.el .IP "\f(CWgsl_sf_coupling_9j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji, $result)\fR" 4
.IX Item "gsl_sf_coupling_9j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji, $result)"
.ie n .IP """gsl_sf_coupling_9j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji)""" 4
.el .IP "\f(CWgsl_sf_coupling_9j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji)\fR" 4
.IX Item "gsl_sf_coupling_9j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji)"
.PD
These routines compute the Wigner 9\-j coefficient,
.Sp
.Vb 4
\&          {ja jb jc
\&           jd je jf
\&           jg jh ji}
\& where the arguments are given in half\-integer units, ja = two_ja/2, ma = two_ma/2, etc.
.Ve
.ie n .IP """gsl_sf_dawson_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_dawson_e($x, $result)\fR" 4
.IX Item "gsl_sf_dawson_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_dawson($x)""" 4
.el .IP "\f(CWgsl_sf_dawson($x)\fR" 4
.IX Item "gsl_sf_dawson($x)"
.PD
These routines compute the value of Dawson's integral for \f(CW$x\fR.
.ie n .IP """gsl_sf_debye_1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_1_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_1($x)""" 4
.el .IP "\f(CWgsl_sf_debye_1($x)\fR" 4
.IX Item "gsl_sf_debye_1($x)"
.PD
These routines compute the first-order Debye function D_1(x) = (1/x) \eint_0^x dt (t/(e^t \- 1)).
.ie n .IP """gsl_sf_debye_2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_2_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_2_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_2($x)""" 4
.el .IP "\f(CWgsl_sf_debye_2($x)\fR" 4
.IX Item "gsl_sf_debye_2($x)"
.PD
These routines compute the second-order Debye function D_2(x) = (2/x^2) \eint_0^x dt (t^2/(e^t \- 1)).
.ie n .IP """gsl_sf_debye_3_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_3_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_3_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_3($x)""" 4
.el .IP "\f(CWgsl_sf_debye_3($x)\fR" 4
.IX Item "gsl_sf_debye_3($x)"
.PD
These routines compute the third-order Debye function D_3(x) = (3/x^3) \eint_0^x dt (t^3/(e^t \- 1)).
.ie n .IP """gsl_sf_debye_4_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_4_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_4_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_4($x)""" 4
.el .IP "\f(CWgsl_sf_debye_4($x)\fR" 4
.IX Item "gsl_sf_debye_4($x)"
.PD
These routines compute the fourth-order Debye function D_4(x) = (4/x^4) \eint_0^x dt (t^4/(e^t \- 1)).
.ie n .IP """gsl_sf_debye_5_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_5_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_5_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_5($x)""" 4
.el .IP "\f(CWgsl_sf_debye_5($x)\fR" 4
.IX Item "gsl_sf_debye_5($x)"
.PD
These routines compute the fifth-order Debye function D_5(x) = (5/x^5) \eint_0^x dt (t^5/(e^t \- 1)).
.ie n .IP """gsl_sf_debye_6_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_debye_6_e($x, $result)\fR" 4
.IX Item "gsl_sf_debye_6_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_debye_6($x)""" 4
.el .IP "\f(CWgsl_sf_debye_6($x)\fR" 4
.IX Item "gsl_sf_debye_6($x)"
.PD
These routines compute the sixth-order Debye function D_6(x) = (6/x^6) \eint_0^x dt (t^6/(e^t \- 1)).
.ie n .IP """gsl_sf_dilog_e ($x, $result)""" 4
.el .IP "\f(CWgsl_sf_dilog_e ($x, $result)\fR" 4
.IX Item "gsl_sf_dilog_e ($x, $result)"
.PD 0
.ie n .IP """gsl_sf_dilog($x)""" 4
.el .IP "\f(CWgsl_sf_dilog($x)\fR" 4
.IX Item "gsl_sf_dilog($x)"
.PD
.Vb 1
\& These routines compute the dilogarithm for a real argument. In Lewin\*(Aqs notation this is Li_2(x), the real part of the dilogarithm of a real x. It is defined by the integral representation Li_2(x) = \- \eRe \eint_0^x ds \elog(1\-s) / s. Note that \eIm(Li_2(x)) = 0 for x <= 1, and \-\epi\elog(x) for x > 1. Note that Abramowitz & Stegun refer to the Spence integral S(x)=Li_2(1\-x) as the dilogarithm rather than Li_2(x).
.Ve
.ie n .IP """gsl_sf_complex_dilog_xy_e"" \-" 4
.el .IP "\f(CWgsl_sf_complex_dilog_xy_e\fR \-" 4
.IX Item "gsl_sf_complex_dilog_xy_e -"
.PD 0
.ie n .IP """gsl_sf_complex_dilog_e($r, $theta, $result_re, $result_im)"" \- This function computes the full complex-valued dilogarithm for the complex argument z = r \eexp(i \etheta). The real and imaginary parts of the result are returned in the $result_re and $result_im gsl_result structs." 4
.el .IP "\f(CWgsl_sf_complex_dilog_e($r, $theta, $result_re, $result_im)\fR \- This function computes the full complex-valued dilogarithm for the complex argument z = r \eexp(i \etheta). The real and imaginary parts of the result are returned in the \f(CW$result_re\fR and \f(CW$result_im\fR gsl_result structs." 4
.IX Item "gsl_sf_complex_dilog_e($r, $theta, $result_re, $result_im) - This function computes the full complex-valued dilogarithm for the complex argument z = r exp(i theta). The real and imaginary parts of the result are returned in the $result_re and $result_im gsl_result structs."
.ie n .IP """gsl_sf_complex_spence_xy_e"" \-" 4
.el .IP "\f(CWgsl_sf_complex_spence_xy_e\fR \-" 4
.IX Item "gsl_sf_complex_spence_xy_e -"
.ie n .IP """gsl_sf_multiply""" 4
.el .IP "\f(CWgsl_sf_multiply\fR" 4
.IX Item "gsl_sf_multiply"
.ie n .IP """gsl_sf_multiply_e($x, $y, $result)"" \- This function multiplies $x and $y storing the product and its associated error in $result." 4
.el .IP "\f(CWgsl_sf_multiply_e($x, $y, $result)\fR \- This function multiplies \f(CW$x\fR and \f(CW$y\fR storing the product and its associated error in \f(CW$result\fR." 4
.IX Item "gsl_sf_multiply_e($x, $y, $result) - This function multiplies $x and $y storing the product and its associated error in $result."
.ie n .IP """gsl_sf_multiply_err_e($x, $dx, $y, $dy, $result)"" \- This function multiplies $x and $y with associated absolute errors $dx and $dy. The product xy +/\- xy \esqrt((dx/x)^2 +(dy/y)^2) is stored in $result." 4
.el .IP "\f(CWgsl_sf_multiply_err_e($x, $dx, $y, $dy, $result)\fR \- This function multiplies \f(CW$x\fR and \f(CW$y\fR with associated absolute errors \f(CW$dx\fR and \f(CW$dy\fR. The product xy +/\- xy \esqrt((dx/x)^2 +(dy/y)^2) is stored in \f(CW$result\fR." 4
.IX Item "gsl_sf_multiply_err_e($x, $dx, $y, $dy, $result) - This function multiplies $x and $y with associated absolute errors $dx and $dy. The product xy +/- xy sqrt((dx/x)^2 +(dy/y)^2) is stored in $result."
.ie n .IP """gsl_sf_ellint_Kcomp_e($k, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_Kcomp_e($k, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_Kcomp_e($k, $mode, $result)"
.ie n .IP """gsl_sf_ellint_Kcomp($k, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_Kcomp($k, $mode)\fR" 4
.IX Item "gsl_sf_ellint_Kcomp($k, $mode)"
.PD
These routines compute the complete elliptic integral K($k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
.ie n .IP """gsl_sf_ellint_Ecomp_e($k, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_Ecomp_e($k, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_Ecomp_e($k, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_Ecomp($k, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_Ecomp($k, $mode)\fR" 4
.IX Item "gsl_sf_ellint_Ecomp($k, $mode)"
.ie n .IP """gsl_sf_ellint_Pcomp_e($k, $n, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_Pcomp_e($k, $n, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_Pcomp_e($k, $n, $mode, $result)"
.ie n .IP """gsl_sf_ellint_Pcomp($k, $n, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_Pcomp($k, $n, $mode)\fR" 4
.IX Item "gsl_sf_ellint_Pcomp($k, $n, $mode)"
.ie n .IP """gsl_sf_ellint_Dcomp_e""" 4
.el .IP "\f(CWgsl_sf_ellint_Dcomp_e\fR" 4
.IX Item "gsl_sf_ellint_Dcomp_e"
.ie n .IP """gsl_sf_ellint_Dcomp """ 4
.el .IP "\f(CWgsl_sf_ellint_Dcomp \fR" 4
.IX Item "gsl_sf_ellint_Dcomp "
.ie n .IP """gsl_sf_ellint_F_e($phi, $k, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_F_e($phi, $k, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_F_e($phi, $k, $mode, $result)"
.ie n .IP """gsl_sf_ellint_F($phi, $k, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_F($phi, $k, $mode)\fR" 4
.IX Item "gsl_sf_ellint_F($phi, $k, $mode)"
.PD
These routines compute the incomplete elliptic integral F($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
.ie n .IP """gsl_sf_ellint_E_e($phi, $k, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_E_e($phi, $k, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_E_e($phi, $k, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_E($phi, $k, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_E($phi, $k, $mode)\fR" 4
.IX Item "gsl_sf_ellint_E($phi, $k, $mode)"
.PD
These routines compute the incomplete elliptic integral E($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
.ie n .IP """gsl_sf_ellint_P_e($phi, $k, $n, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_P_e($phi, $k, $n, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_P_e($phi, $k, $n, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_P($phi, $k, $n, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_P($phi, $k, $n, $mode)\fR" 4
.IX Item "gsl_sf_ellint_P($phi, $k, $n, $mode)"
.PD
These routines compute the incomplete elliptic integral \ePi(\ephi,k,n) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \esin^2(\ealpha) = k^2, with the change of sign n \eto \-n.
.ie n .IP """gsl_sf_ellint_D_e($phi, $k, $n, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_D_e($phi, $k, $n, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_D_e($phi, $k, $n, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_D($phi, $k, $n, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_D($phi, $k, $n, $mode)\fR" 4
.IX Item "gsl_sf_ellint_D($phi, $k, $n, $mode)"
.PD
These functions compute the incomplete elliptic integral D(\ephi,k) which is defined through the Carlson form \s-1RD\s0(x,y,z) by the following relation, D(\ephi,k,n) = (1/3)(\esin(\ephi))^3 \s-1RD\s0 (1\-\esin^2(\ephi), 1\-k^2 \esin^2(\ephi), 1). The argument \f(CW$n\fR is not used and will be removed in a future release.
.ie n .IP """gsl_sf_ellint_RC_e($x, $y, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_RC_e($x, $y, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_RC_e($x, $y, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_RC($x, $y, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_RC($x, $y, $mode)\fR" 4
.IX Item "gsl_sf_ellint_RC($x, $y, $mode)"
.PD
.Vb 1
\& These routines compute the incomplete elliptic integral RC($x,$y) to the accuracy specified by the mode variable $mode.
.Ve
.ie n .IP """gsl_sf_ellint_RD_e($x, $y, $z, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_RD_e($x, $y, $z, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_RD_e($x, $y, $z, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_RD($x, $y, $z, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_RD($x, $y, $z, $mode)\fR" 4
.IX Item "gsl_sf_ellint_RD($x, $y, $z, $mode)"
.PD
.Vb 1
\& These routines compute the incomplete elliptic integral RD($x,$y,$z) to the accuracy specified by the mode variable $mode.
.Ve
.ie n .IP """gsl_sf_ellint_RF_e($x, $y, $z, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_RF_e($x, $y, $z, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_RF_e($x, $y, $z, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_RF($x, $y, $z, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_RF($x, $y, $z, $mode)\fR" 4
.IX Item "gsl_sf_ellint_RF($x, $y, $z, $mode)"
.PD
.Vb 1
\& These routines compute the incomplete elliptic integral RF($x,$y,$z) to the accuracy specified by the mode variable $mode.
.Ve
.ie n .IP """gsl_sf_ellint_RJ_e($x, $y, $z, $p, $mode, $result)""" 4
.el .IP "\f(CWgsl_sf_ellint_RJ_e($x, $y, $z, $p, $mode, $result)\fR" 4
.IX Item "gsl_sf_ellint_RJ_e($x, $y, $z, $p, $mode, $result)"
.PD 0
.ie n .IP """gsl_sf_ellint_RJ($x, $y, $z, $p, $mode)""" 4
.el .IP "\f(CWgsl_sf_ellint_RJ($x, $y, $z, $p, $mode)\fR" 4
.IX Item "gsl_sf_ellint_RJ($x, $y, $z, $p, $mode)"
.PD
.Vb 1
\& These routines compute the incomplete elliptic integral RJ($x,$y,$z,$p) to the accuracy specified by the mode variable $mode.
.Ve
.ie n .IP """gsl_sf_elljac_e($u, $m)"" \- This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeeded, 1 otherwise and then returns the result of sn, cn and dn in this order." 4
.el .IP "\f(CWgsl_sf_elljac_e($u, $m)\fR \- This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeeded, 1 otherwise and then returns the result of sn, cn and dn in this order." 4
.IX Item "gsl_sf_elljac_e($u, $m) - This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeeded, 1 otherwise and then returns the result of sn, cn and dn in this order."
.PD 0
.ie n .IP """gsl_sf_erfc_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_erfc_e($x, $result)\fR" 4
.IX Item "gsl_sf_erfc_e($x, $result)"
.ie n .IP """gsl_sf_erfc($x)""" 4
.el .IP "\f(CWgsl_sf_erfc($x)\fR" 4
.IX Item "gsl_sf_erfc($x)"
.PD
These routines compute the complementary error function erfc(x) = 1 \- erf(x) = (2/\esqrt(\epi)) \eint_x^\einfty \eexp(\-t^2).
.ie n .IP """gsl_sf_log_erfc_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_log_erfc_e($x, $result)\fR" 4
.IX Item "gsl_sf_log_erfc_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_log_erfc($x)""" 4
.el .IP "\f(CWgsl_sf_log_erfc($x)\fR" 4
.IX Item "gsl_sf_log_erfc($x)"
.PD
These routines compute the logarithm of the complementary error function \elog(\eerfc(x)).
.ie n .IP """gsl_sf_erf_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_erf_e($x, $result)\fR" 4
.IX Item "gsl_sf_erf_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_erf($x)""" 4
.el .IP "\f(CWgsl_sf_erf($x)\fR" 4
.IX Item "gsl_sf_erf($x)"
.PD
These routines compute the error function erf(x), where erf(x) = (2/\esqrt(\epi)) \eint_0^x dt \eexp(\-t^2).
.ie n .IP """gsl_sf_erf_Z_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_erf_Z_e($x, $result)\fR" 4
.IX Item "gsl_sf_erf_Z_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_erf_Z($x)""" 4
.el .IP "\f(CWgsl_sf_erf_Z($x)\fR" 4
.IX Item "gsl_sf_erf_Z($x)"
.PD
These routines compute the Gaussian probability density function Z(x) = (1/\esqrt{2\epi}) \eexp(\-x^2/2).
.ie n .IP """gsl_sf_erf_Q_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_erf_Q_e($x, $result)\fR" 4
.IX Item "gsl_sf_erf_Q_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_erf_Q($x)""" 4
.el .IP "\f(CWgsl_sf_erf_Q($x)\fR" 4
.IX Item "gsl_sf_erf_Q($x)"
.PD
.Vb 1
\& These routines compute the upper tail of the Gaussian probability function Q(x) = (1/\esqrt{2\epi}) \eint_x^\einfty dt \eexp(\-t^2/2). The hazard function for the normal distribution, also known as the inverse Mill\*(Aqs ratio, is defined as, h(x) = Z(x)/Q(x) = \esqrt{2/\epi} \eexp(\-x^2 / 2) / \eerfc(x/\esqrt 2) It decreases rapidly as x approaches \-\einfty and asymptotes to h(x) \esim x as x approaches +\einfty.
.Ve
.ie n .IP """gsl_sf_hazard_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_hazard_e($x, $result)\fR" 4
.IX Item "gsl_sf_hazard_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_hazard($x)""" 4
.el .IP "\f(CWgsl_sf_hazard($x)\fR" 4
.IX Item "gsl_sf_hazard($x)"
.PD
.Vb 1
\& These routines compute the hazard function for the normal distribution.
.Ve
.ie n .IP """gsl_sf_exp_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_exp_e($x, $result)\fR" 4
.IX Item "gsl_sf_exp_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_exp($x)""" 4
.el .IP "\f(CWgsl_sf_exp($x)\fR" 4
.IX Item "gsl_sf_exp($x)"
.PD
.Vb 1
\& These routines provide an exponential function \eexp(x) using GSL semantics and error checking.
.Ve
.ie n .IP """gsl_sf_exp_e10_e"" \-" 4
.el .IP "\f(CWgsl_sf_exp_e10_e\fR \-" 4
.IX Item "gsl_sf_exp_e10_e -"
.PD 0
.ie n .IP """gsl_sf_exp_mult_e """ 4
.el .IP "\f(CWgsl_sf_exp_mult_e \fR" 4
.IX Item "gsl_sf_exp_mult_e "
.ie n .IP """gsl_sf_exp_mult""" 4
.el .IP "\f(CWgsl_sf_exp_mult\fR" 4
.IX Item "gsl_sf_exp_mult"
.ie n .IP """gsl_sf_exp_mult_e10_e"" \-" 4
.el .IP "\f(CWgsl_sf_exp_mult_e10_e\fR \-" 4
.IX Item "gsl_sf_exp_mult_e10_e -"
.ie n .IP """gsl_sf_expm1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_expm1_e($x, $result)\fR" 4
.IX Item "gsl_sf_expm1_e($x, $result)"
.ie n .IP """gsl_sf_expm1($x)""" 4
.el .IP "\f(CWgsl_sf_expm1($x)\fR" 4
.IX Item "gsl_sf_expm1($x)"
.PD
These routines compute the quantity \eexp(x)\-1 using an algorithm that is accurate for small x.
.ie n .IP """gsl_sf_exprel_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_exprel_e($x, $result)\fR" 4
.IX Item "gsl_sf_exprel_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_exprel($x)""" 4
.el .IP "\f(CWgsl_sf_exprel($x)\fR" 4
.IX Item "gsl_sf_exprel($x)"
.PD
These routines compute the quantity (\eexp(x)\-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\eexp(x)\-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \edots.
.ie n .IP """gsl_sf_exprel_2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_exprel_2_e($x, $result)\fR" 4
.IX Item "gsl_sf_exprel_2_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_exprel_2($x)""" 4
.el .IP "\f(CWgsl_sf_exprel_2($x)\fR" 4
.IX Item "gsl_sf_exprel_2($x)"
.PD
These routines compute the quantity 2(\eexp(x)\-1\-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\eexp(x)\-1\-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \edots.
.ie n .IP """gsl_sf_exprel_n_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_exprel_n_e($x, $result)\fR" 4
.IX Item "gsl_sf_exprel_n_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_exprel_n($x)""" 4
.el .IP "\f(CWgsl_sf_exprel_n($x)\fR" 4
.IX Item "gsl_sf_exprel_n($x)"
.PD
These routines compute the N\-relative exponential, which is the n\-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N\-relative exponential is given by,
 exprel_N(x) = N!/x^N (\eexp(x) \- \esum_{k=0}^{N\-1} x^k/k!)
  = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ...
  = 1F1 (1,1+N,x)
.ie n .IP """gsl_sf_exp_err_e($x, $dx, $result)"" \- This function exponentiates $x with an associated absolute error $dx." 4
.el .IP "\f(CWgsl_sf_exp_err_e($x, $dx, $result)\fR \- This function exponentiates \f(CW$x\fR with an associated absolute error \f(CW$dx\fR." 4
.IX Item "gsl_sf_exp_err_e($x, $dx, $result) - This function exponentiates $x with an associated absolute error $dx."
.PD 0
.ie n .IP """gsl_sf_exp_err_e10_e"" \-" 4
.el .IP "\f(CWgsl_sf_exp_err_e10_e\fR \-" 4
.IX Item "gsl_sf_exp_err_e10_e -"
.ie n .IP """gsl_sf_exp_mult_err_e($x, $dx, $y, $dy, $result)"" \-" 4
.el .IP "\f(CWgsl_sf_exp_mult_err_e($x, $dx, $y, $dy, $result)\fR \-" 4
.IX Item "gsl_sf_exp_mult_err_e($x, $dx, $y, $dy, $result) -"
.ie n .IP """gsl_sf_exp_mult_err_e10_e"" \-" 4
.el .IP "\f(CWgsl_sf_exp_mult_err_e10_e\fR \-" 4
.IX Item "gsl_sf_exp_mult_err_e10_e -"
.ie n .IP """gsl_sf_expint_E1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_expint_E1_e($x, $result)\fR" 4
.IX Item "gsl_sf_expint_E1_e($x, $result)"
.ie n .IP """gsl_sf_expint_E1($x)""" 4
.el .IP "\f(CWgsl_sf_expint_E1($x)\fR" 4
.IX Item "gsl_sf_expint_E1($x)"
.PD
These routines compute the exponential integral E_1(x), E_1(x) := \eRe \eint_1^\einfty dt \eexp(\-xt)/t.
.ie n .IP """gsl_sf_expint_E2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_expint_E2_e($x, $result)\fR" 4
.IX Item "gsl_sf_expint_E2_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_expint_E2($x)""" 4
.el .IP "\f(CWgsl_sf_expint_E2($x)\fR" 4
.IX Item "gsl_sf_expint_E2($x)"
.PD
These routines compute the second-order exponential integral E_2(x),
  E_2(x) := \eRe \eint_1^\einfty dt \eexp(\-xt)/t^2.
.ie n .IP """gsl_sf_expint_En_e($n, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_expint_En_e($n, $x, $result)\fR" 4
.IX Item "gsl_sf_expint_En_e($n, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_expint_En($n, $x)""" 4
.el .IP "\f(CWgsl_sf_expint_En($n, $x)\fR" 4
.IX Item "gsl_sf_expint_En($n, $x)"
.PD
These routines compute the exponential integral E_n(x) of order n,
  E_n(x) := \eRe \eint_1^\einfty dt \eexp(\-xt)/t^n.
.ie n .IP """gsl_sf_expint_E1_scaled_e """ 4
.el .IP "\f(CWgsl_sf_expint_E1_scaled_e \fR" 4
.IX Item "gsl_sf_expint_E1_scaled_e "
.PD 0
.ie n .IP """gsl_sf_expint_E1_scaled""" 4
.el .IP "\f(CWgsl_sf_expint_E1_scaled\fR" 4
.IX Item "gsl_sf_expint_E1_scaled"
.ie n .IP """gsl_sf_expint_E2_scaled_e""" 4
.el .IP "\f(CWgsl_sf_expint_E2_scaled_e\fR" 4
.IX Item "gsl_sf_expint_E2_scaled_e"
.ie n .IP """gsl_sf_expint_E2_scaled """ 4
.el .IP "\f(CWgsl_sf_expint_E2_scaled \fR" 4
.IX Item "gsl_sf_expint_E2_scaled "
.ie n .IP """gsl_sf_expint_En_scaled_e""" 4
.el .IP "\f(CWgsl_sf_expint_En_scaled_e\fR" 4
.IX Item "gsl_sf_expint_En_scaled_e"
.ie n .IP """gsl_sf_expint_En_scaled""" 4
.el .IP "\f(CWgsl_sf_expint_En_scaled\fR" 4
.IX Item "gsl_sf_expint_En_scaled"
.ie n .IP """gsl_sf_expint_Ei_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_expint_Ei_e($x, $result)\fR" 4
.IX Item "gsl_sf_expint_Ei_e($x, $result)"
.ie n .IP """gsl_sf_expint_Ei($x)""" 4
.el .IP "\f(CWgsl_sf_expint_Ei($x)\fR" 4
.IX Item "gsl_sf_expint_Ei($x)"
.PD
These routines compute the exponential integral Ei(x), Ei(x) := \- \s-1PV\s0(\eint_{\-x}^\einfty dt \eexp(\-t)/t) where \s-1PV\s0 denotes the principal value of the integral.
.ie n .IP """gsl_sf_expint_Ei_scaled_e""" 4
.el .IP "\f(CWgsl_sf_expint_Ei_scaled_e\fR" 4
.IX Item "gsl_sf_expint_Ei_scaled_e"
.PD 0
.ie n .IP """gsl_sf_expint_Ei_scaled """ 4
.el .IP "\f(CWgsl_sf_expint_Ei_scaled \fR" 4
.IX Item "gsl_sf_expint_Ei_scaled "
.ie n .IP """gsl_sf_Shi_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_Shi_e($x, $result)\fR" 4
.IX Item "gsl_sf_Shi_e($x, $result)"
.ie n .IP """gsl_sf_Shi($x)""" 4
.el .IP "\f(CWgsl_sf_Shi($x)\fR" 4
.IX Item "gsl_sf_Shi($x)"
.PD
These routines compute the integral Shi(x) = \eint_0^x dt \esinh(t)/t.
.ie n .IP """gsl_sf_Chi_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_Chi_e($x, $result)\fR" 4
.IX Item "gsl_sf_Chi_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_Chi($x)""" 4
.el .IP "\f(CWgsl_sf_Chi($x)\fR" 4
.IX Item "gsl_sf_Chi($x)"
.PD
These routines compute the integral Chi(x) := \eRe[ \egamma_E + \elog(x) + \eint_0^x dt (\ecosh[t]\-1)/t] , where \egamma_E is the Euler constant (available as \f(CW$M_EULER\fR from the Math::GSL::Const module).
.ie n .IP """gsl_sf_expint_3_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_expint_3_e($x, $result)\fR" 4
.IX Item "gsl_sf_expint_3_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_expint_3($x)""" 4
.el .IP "\f(CWgsl_sf_expint_3($x)\fR" 4
.IX Item "gsl_sf_expint_3($x)"
.PD
These routines compute the third-order exponential integral Ei_3(x) = \eint_0^xdt \eexp(\-t^3) for x >= 0.
.ie n .IP """gsl_sf_Si_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_Si_e($x, $result)\fR" 4
.IX Item "gsl_sf_Si_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_Si($x)""" 4
.el .IP "\f(CWgsl_sf_Si($x)\fR" 4
.IX Item "gsl_sf_Si($x)"
.PD
These routines compute the Sine integral Si(x) = \eint_0^x dt \esin(t)/t.
.ie n .IP """gsl_sf_Ci_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_Ci_e($x, $result)\fR" 4
.IX Item "gsl_sf_Ci_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_Ci($x)""" 4
.el .IP "\f(CWgsl_sf_Ci($x)\fR" 4
.IX Item "gsl_sf_Ci($x)"
.PD
These routines compute the Cosine integral Ci(x) = \-\eint_x^\einfty dt \ecos(t)/t for x > 0.
.ie n .IP """gsl_sf_fermi_dirac_m1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_m1_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_m1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_m1($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_m1($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_m1($x)"
.PD
These routines compute the complete Fermi-Dirac integral with an index of \-1. This integral is given by F_{\-1}(x) = e^x / (1 + e^x).
.ie n .IP """gsl_sf_fermi_dirac_0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_0_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_0($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_0($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_0($x)"
.PD
These routines compute the complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = \eln(1 + e^x).
.ie n .IP """gsl_sf_fermi_dirac_1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_1_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_1($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_1($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_1($x)"
.PD
These routines compute the complete Fermi-Dirac integral with an index of 1, F_1(x) = \eint_0^\einfty dt (t /(\eexp(t\-x)+1)).
.ie n .IP """gsl_sf_fermi_dirac_2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_2_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_2_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_2($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_2($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_2($x)"
.PD
These routines compute the complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \eint_0^\einfty dt (t^2 /(\eexp(t\-x)+1)).
.ie n .IP """gsl_sf_fermi_dirac_int_e($j, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_int_e($j, $x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_int_e($j, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_int($j, $x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_int($j, $x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_int($j, $x)"
.PD
These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\eGamma(j+1)) \eint_0^\einfty dt (t^j /(\eexp(t\-x)+1)).
.ie n .IP """gsl_sf_fermi_dirac_mhalf_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_mhalf_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_mhalf_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_mhalf($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_mhalf($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_mhalf($x)"
.PD
These routines compute the complete Fermi-Dirac integral F_{\-1/2}(x).
.ie n .IP """gsl_sf_fermi_dirac_half_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_half_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_half_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_half($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_half($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_half($x)"
.PD
These routines compute the complete Fermi-Dirac integral F_{1/2}(x).
.ie n .IP """gsl_sf_fermi_dirac_3half_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_3half_e($x, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_3half_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_3half($x)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_3half($x)\fR" 4
.IX Item "gsl_sf_fermi_dirac_3half($x)"
.PD
These routines compute the complete Fermi-Dirac integral F_{3/2}(x).
.ie n .IP """gsl_sf_fermi_dirac_inc_0_e($x, $b, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_inc_0_e($x, $b, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_inc_0_e($x, $b, $result)"
.PD 0
.ie n .IP """gsl_sf_fermi_dirac_inc_0($x, $b, $result)""" 4
.el .IP "\f(CWgsl_sf_fermi_dirac_inc_0($x, $b, $result)\fR" 4
.IX Item "gsl_sf_fermi_dirac_inc_0($x, $b, $result)"
.PD
These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \eln(1 + e^{b\-x}) \- (b\-x).
.ie n .IP """gsl_sf_legendre_Pl_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_Pl_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_legendre_Pl_e($l, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_legendre_Pl($l, $x)""" 4
.el .IP "\f(CWgsl_sf_legendre_Pl($l, $x)\fR" 4
.IX Item "gsl_sf_legendre_Pl($l, $x)"
.PD
These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1
.ie n .IP """gsl_sf_legendre_Pl_array""" 4
.el .IP "\f(CWgsl_sf_legendre_Pl_array\fR" 4
.IX Item "gsl_sf_legendre_Pl_array"
.PD 0
.ie n .IP """gsl_sf_legendre_Pl_deriv_array""" 4
.el .IP "\f(CWgsl_sf_legendre_Pl_deriv_array\fR" 4
.IX Item "gsl_sf_legendre_Pl_deriv_array"
.ie n .IP """gsl_sf_legendre_P1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_P1_e($x, $result)\fR" 4
.IX Item "gsl_sf_legendre_P1_e($x, $result)"
.ie n .IP """gsl_sf_legendre_P2_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_P2_e($x, $result)\fR" 4
.IX Item "gsl_sf_legendre_P2_e($x, $result)"
.ie n .IP """gsl_sf_legendre_P3_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_P3_e($x, $result)\fR" 4
.IX Item "gsl_sf_legendre_P3_e($x, $result)"
.ie n .IP """gsl_sf_legendre_P1($x)""" 4
.el .IP "\f(CWgsl_sf_legendre_P1($x)\fR" 4
.IX Item "gsl_sf_legendre_P1($x)"
.ie n .IP """gsl_sf_legendre_P2($x)""" 4
.el .IP "\f(CWgsl_sf_legendre_P2($x)\fR" 4
.IX Item "gsl_sf_legendre_P2($x)"
.ie n .IP """gsl_sf_legendre_P3($x)""" 4
.el .IP "\f(CWgsl_sf_legendre_P3($x)\fR" 4
.IX Item "gsl_sf_legendre_P3($x)"
.PD
These functions evaluate the Legendre polynomials P_l(x) using explicit representations for l=1, 2, 3.
.ie n .IP """gsl_sf_legendre_Q0_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_Q0_e($x, $result)\fR" 4
.IX Item "gsl_sf_legendre_Q0_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_legendre_Q0($x)""" 4
.el .IP "\f(CWgsl_sf_legendre_Q0($x)\fR" 4
.IX Item "gsl_sf_legendre_Q0($x)"
.PD
These routines compute the Legendre function Q_0(x) for x > \-1, x != 1.
.ie n .IP """gsl_sf_legendre_Q1_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_Q1_e($x, $result)\fR" 4
.IX Item "gsl_sf_legendre_Q1_e($x, $result)"
.PD 0
.ie n .IP """gsl_sf_legendre_Q1($x)""" 4
.el .IP "\f(CWgsl_sf_legendre_Q1($x)\fR" 4
.IX Item "gsl_sf_legendre_Q1($x)"
.PD
These routines compute the Legendre function Q_1(x) for x > \-1, x != 1.
.ie n .IP """gsl_sf_legendre_Ql_e($l, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_Ql_e($l, $x, $result)\fR" 4
.IX Item "gsl_sf_legendre_Ql_e($l, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_legendre_Ql($l, $x)""" 4
.el .IP "\f(CWgsl_sf_legendre_Ql($l, $x)\fR" 4
.IX Item "gsl_sf_legendre_Ql($l, $x)"
.PD
These routines compute the Legendre function Q_l(x) for x > \-1, x != 1 and l >= 0.
.ie n .IP """gsl_sf_legendre_Plm_e($l, $m, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_Plm_e($l, $m, $x, $result)\fR" 4
.IX Item "gsl_sf_legendre_Plm_e($l, $m, $x, $result)"
.PD 0
.ie n .IP """gsl_sf_legendre_Plm($l, $m, $x)""" 4
.el .IP "\f(CWgsl_sf_legendre_Plm($l, $m, $x)\fR" 4
.IX Item "gsl_sf_legendre_Plm($l, $m, $x)"
.PD
These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1.
.ie n .IP """gsl_sf_legendre_Plm_array""" 4
.el .IP "\f(CWgsl_sf_legendre_Plm_array\fR" 4
.IX Item "gsl_sf_legendre_Plm_array"
.PD 0
.ie n .IP """gsl_sf_legendre_Plm_deriv_array """ 4
.el .IP "\f(CWgsl_sf_legendre_Plm_deriv_array \fR" 4
.IX Item "gsl_sf_legendre_Plm_deriv_array "
.ie n .IP """gsl_sf_legendre_sphPlm_e($l, $m, $x, $result)""" 4
.el .IP "\f(CWgsl_sf_legendre_sphPlm_e($l, $m, $x, $result)\fR" 4
.IX Item "gsl_sf_legendre_sphPlm_e($l, $m, $x, $result)"
.ie n .IP """gsl_sf_legendre_sphPlm($l, $m, $x)""" 4
.el .IP "\f(CWgsl_sf_legendre_sphPlm($l, $m, $x)\fR" 4
.IX Item "gsl_sf_legendre_sphPlm($l, $m, $x)"
.PD
These routines compute the normalized associated Legendre polynomial $\esqrt{(2l+1)/(4\epi)} \esqrt{(l\-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x).
.ie n .IP """gsl_sf_legendre_sphPlm_array """ 4
.el .IP "\f(CWgsl_sf_legendre_sphPlm_array \fR" 4
.IX Item "gsl_sf_legendre_sphPlm_array "
.PD 0
.ie n .IP """gsl_sf_legendre_sphPlm_deriv_array""" 4
.el .IP "\f(CWgsl_sf_legendre_sphPlm_deriv_array\fR" 4
.IX Item "gsl_sf_legendre_sphPlm_deriv_array"
.ie n .IP """gsl_sf_legendre_array_size"" \-" 4
.el .IP "\f(CWgsl_sf_legendre_array_size\fR \-" 4
.IX Item "gsl_sf_legendre_array_size -"
.ie n .IP """gsl_sf_lngamma_e($x, $result)""" 4
.el .IP "\f(CWgsl_sf_lngamma_e($x, $result)\fR" 4
.IX Item "gsl_sf_lngamma_e($x, $result)"
.ie n .IP """gsl_sf_lngamma($x)""" 4
.el .IP "\f(CWgsl_sf_lngamma($x)\fR" 4
.IX Item "gsl_sf_lngamma($x)"
.PD
These routines compute the logarithm of the Gamma function, \elog(\eGamma(x)), subject to x not being a negative integer or zero. For x<0 the real part of \elog(\eGamma(x)) is returned, which is equivalent to \elog(|\eGamma(x)|). The function is computed using the real Lanczos method.
.ie n .IP """gsl_sf_lngamma_sgn_e($x, $result_lg)"" \- This routine returns the sign of the gamma function and the logarithm of its magnitude into this order, subject to $x not being a negative integer or zero. The function is computed using the real Lanczos method. The value of the gamma function can be reconstructed using the relation \eGamma(x) = sgn * \eexp(resultlg)." 4
.el .IP "\f(CWgsl_sf_lngamma_sgn_e($x, $result_lg)\fR \- This routine returns the sign of the gamma function and the logarithm of its magnitude into this order, subject to \f(CW$x\fR not being a negative integer or zero. The function is computed using the real Lanczos method. The value of the gamma function can be reconstructed using the relation \eGamma(x) = sgn * \eexp(resultlg)." 4
.IX Item "gsl_sf_lngamma_sgn_e($x, $result_lg) - This routine returns the sign of the gamma function and the logarithm of its magnitude into this order, subject to $x not being a negative integer or zero. The function is computed using the real Lanczos method. The value of the gamma function can be reconstructed using the relation Gamma(x) = sgn * exp(resultlg)."
.PD 0
.ie n .IP """gsl_sf_gamma_e """ 4
.el .IP "\f(CWgsl_sf_gamma_e \fR" 4
.IX Item "gsl_sf_gamma_e "
.ie n .IP """gsl_sf_gamma""" 4
.el .IP "\f(CWgsl_sf_gamma\fR" 4
.IX Item "gsl_sf_gamma"
.ie n .IP """gsl_sf_gammastar_e""" 4
.el .IP "\f(CWgsl_sf_gammastar_e\fR" 4
.IX Item "gsl_sf_gammastar_e"
.ie n .IP """gsl_sf_gammastar """ 4
.el .IP "\f(CWgsl_sf_gammastar \fR" 4
.IX Item "gsl_sf_gammastar "
.ie n .IP """gsl_sf_gammainv_e""" 4
.el .IP "\f(CWgsl_sf_gammainv_e\fR" 4
.IX Item "gsl_sf_gammainv_e"
.ie n .IP """gsl_sf_gammainv""" 4
.el .IP "\f(CWgsl_sf_gammainv\fR" 4
.IX Item "gsl_sf_gammainv"
.ie n .IP """gsl_sf_lngamma_complex_e """ 4
.el .IP "\f(CWgsl_sf_lngamma_complex_e \fR" 4
.IX Item "gsl_sf_lngamma_complex_e "
.ie n .IP """gsl_sf_gamma_inc_Q_e""" 4
.el .IP "\f(CWgsl_sf_gamma_inc_Q_e\fR" 4
.IX Item "gsl_sf_gamma_inc_Q_e"
.ie n .IP """gsl_sf_gamma_inc_Q""" 4
.el .IP "\f(CWgsl_sf_gamma_inc_Q\fR" 4
.IX Item "gsl_sf_gamma_inc_Q"
.ie n .IP """gsl_sf_gamma_inc_P_e """ 4
.el .IP "\f(CWgsl_sf_gamma_inc_P_e \fR" 4
.IX Item "gsl_sf_gamma_inc_P_e "
.ie n .IP """gsl_sf_gamma_inc_P""" 4
.el .IP "\f(CWgsl_sf_gamma_inc_P\fR" 4
.IX Item "gsl_sf_gamma_inc_P"
.ie n .IP """gsl_sf_gamma_inc_e""" 4
.el .IP "\f(CWgsl_sf_gamma_inc_e\fR" 4
.IX Item "gsl_sf_gamma_inc_e"
.ie n .IP """gsl_sf_gamma_inc """ 4
.el .IP "\f(CWgsl_sf_gamma_inc \fR" 4
.IX Item "gsl_sf_gamma_inc "
.ie n .IP """gsl_sf_taylorcoeff_e""" 4
.el .IP "\f(CWgsl_sf_taylorcoeff_e\fR" 4
.IX Item "gsl_sf_taylorcoeff_e"
.ie n .IP """gsl_sf_taylorcoeff""" 4
.el .IP "\f(CWgsl_sf_taylorcoeff\fR" 4
.IX Item "gsl_sf_taylorcoeff"
.ie n .IP """gsl_sf_fact_e """ 4
.el .IP "\f(CWgsl_sf_fact_e \fR" 4
.IX Item "gsl_sf_fact_e "
.ie n .IP """gsl_sf_fact""" 4
.el .IP "\f(CWgsl_sf_fact\fR" 4
.IX Item "gsl_sf_fact"
.ie n .IP """gsl_sf_doublefact_e""" 4
.el .IP "\f(CWgsl_sf_doublefact_e\fR" 4
.IX Item "gsl_sf_doublefact_e"
.ie n .IP """gsl_sf_doublefact """ 4
.el .IP "\f(CWgsl_sf_doublefact \fR" 4
.IX Item "gsl_sf_doublefact "
.ie n .IP """gsl_sf_lnfact_e""" 4
.el .IP "\f(CWgsl_sf_lnfact_e\fR" 4
.IX Item "gsl_sf_lnfact_e"
.ie n .IP """gsl_sf_lnfact""" 4
.el .IP "\f(CWgsl_sf_lnfact\fR" 4
.IX Item "gsl_sf_lnfact"
.ie n .IP """gsl_sf_lndoublefact_e """ 4
.el .IP "\f(CWgsl_sf_lndoublefact_e \fR" 4
.IX Item "gsl_sf_lndoublefact_e "
.ie n .IP """gsl_sf_lndoublefact""" 4
.el .IP "\f(CWgsl_sf_lndoublefact\fR" 4
.IX Item "gsl_sf_lndoublefact"
.ie n .IP """gsl_sf_lnchoose_e""" 4
.el .IP "\f(CWgsl_sf_lnchoose_e\fR" 4
.IX Item "gsl_sf_lnchoose_e"
.ie n .IP """gsl_sf_lnchoose """ 4
.el .IP "\f(CWgsl_sf_lnchoose \fR" 4
.IX Item "gsl_sf_lnchoose "
.ie n .IP """gsl_sf_choose_e""" 4
.el .IP "\f(CWgsl_sf_choose_e\fR" 4
.IX Item "gsl_sf_choose_e"
.ie n .IP """gsl_sf_choose""" 4
.el .IP "\f(CWgsl_sf_choose\fR" 4
.IX Item "gsl_sf_choose"
.ie n .IP """gsl_sf_lnpoch_e """ 4
.el .IP "\f(CWgsl_sf_lnpoch_e \fR" 4
.IX Item "gsl_sf_lnpoch_e "
.ie n .IP """gsl_sf_lnpoch""" 4
.el .IP "\f(CWgsl_sf_lnpoch\fR" 4
.IX Item "gsl_sf_lnpoch"
.ie n .IP """gsl_sf_lnpoch_sgn_e""" 4
.el .IP "\f(CWgsl_sf_lnpoch_sgn_e\fR" 4
.IX Item "gsl_sf_lnpoch_sgn_e"
.ie n .IP """gsl_sf_poch_e """ 4
.el .IP "\f(CWgsl_sf_poch_e \fR" 4
.IX Item "gsl_sf_poch_e "
.ie n .IP """gsl_sf_poch""" 4
.el .IP "\f(CWgsl_sf_poch\fR" 4
.IX Item "gsl_sf_poch"
.ie n .IP """gsl_sf_pochrel_e""" 4
.el .IP "\f(CWgsl_sf_pochrel_e\fR" 4
.IX Item "gsl_sf_pochrel_e"
.ie n .IP """gsl_sf_pochrel """ 4
.el .IP "\f(CWgsl_sf_pochrel \fR" 4
.IX Item "gsl_sf_pochrel "
.ie n .IP """gsl_sf_lnbeta_e""" 4
.el .IP "\f(CWgsl_sf_lnbeta_e\fR" 4
.IX Item "gsl_sf_lnbeta_e"
.ie n .IP """gsl_sf_lnbeta""" 4
.el .IP "\f(CWgsl_sf_lnbeta\fR" 4
.IX Item "gsl_sf_lnbeta"
.ie n .IP """gsl_sf_lnbeta_sgn_e """ 4
.el .IP "\f(CWgsl_sf_lnbeta_sgn_e \fR" 4
.IX Item "gsl_sf_lnbeta_sgn_e "
.ie n .IP """gsl_sf_beta_e""" 4
.el .IP "\f(CWgsl_sf_beta_e\fR" 4
.IX Item "gsl_sf_beta_e"
.ie n .IP """gsl_sf_beta""" 4
.el .IP "\f(CWgsl_sf_beta\fR" 4
.IX Item "gsl_sf_beta"
.ie n .IP """gsl_sf_beta_inc_e """ 4
.el .IP "\f(CWgsl_sf_beta_inc_e \fR" 4
.IX Item "gsl_sf_beta_inc_e "
.ie n .IP """gsl_sf_beta_inc""" 4
.el .IP "\f(CWgsl_sf_beta_inc\fR" 4
.IX Item "gsl_sf_beta_inc"
.ie n .IP """gsl_sf_gegenpoly_1_e""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_1_e\fR" 4
.IX Item "gsl_sf_gegenpoly_1_e"
.ie n .IP """gsl_sf_gegenpoly_2_e """ 4
.el .IP "\f(CWgsl_sf_gegenpoly_2_e \fR" 4
.IX Item "gsl_sf_gegenpoly_2_e "
.ie n .IP """gsl_sf_gegenpoly_3_e""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_3_e\fR" 4
.IX Item "gsl_sf_gegenpoly_3_e"
.ie n .IP """gsl_sf_gegenpoly_1""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_1\fR" 4
.IX Item "gsl_sf_gegenpoly_1"
.ie n .IP """gsl_sf_gegenpoly_2 """ 4
.el .IP "\f(CWgsl_sf_gegenpoly_2 \fR" 4
.IX Item "gsl_sf_gegenpoly_2 "
.ie n .IP """gsl_sf_gegenpoly_3""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_3\fR" 4
.IX Item "gsl_sf_gegenpoly_3"
.ie n .IP """gsl_sf_gegenpoly_n_e""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_n_e\fR" 4
.IX Item "gsl_sf_gegenpoly_n_e"
.ie n .IP """gsl_sf_gegenpoly_n """ 4
.el .IP "\f(CWgsl_sf_gegenpoly_n \fR" 4
.IX Item "gsl_sf_gegenpoly_n "
.ie n .IP """gsl_sf_gegenpoly_array""" 4
.el .IP "\f(CWgsl_sf_gegenpoly_array\fR" 4
.IX Item "gsl_sf_gegenpoly_array"
.ie n .IP """gsl_sf_hyperg_0F1_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_0F1_e\fR" 4
.IX Item "gsl_sf_hyperg_0F1_e"
.ie n .IP """gsl_sf_hyperg_0F1 """ 4
.el .IP "\f(CWgsl_sf_hyperg_0F1 \fR" 4
.IX Item "gsl_sf_hyperg_0F1 "
.ie n .IP """gsl_sf_hyperg_1F1_int_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_1F1_int_e\fR" 4
.IX Item "gsl_sf_hyperg_1F1_int_e"
.ie n .IP """gsl_sf_hyperg_1F1_int""" 4
.el .IP "\f(CWgsl_sf_hyperg_1F1_int\fR" 4
.IX Item "gsl_sf_hyperg_1F1_int"
.ie n .IP """gsl_sf_hyperg_1F1_e """ 4
.el .IP "\f(CWgsl_sf_hyperg_1F1_e \fR" 4
.IX Item "gsl_sf_hyperg_1F1_e "
.ie n .IP """gsl_sf_hyperg_1F1""" 4
.el .IP "\f(CWgsl_sf_hyperg_1F1\fR" 4
.IX Item "gsl_sf_hyperg_1F1"
.ie n .IP """gsl_sf_hyperg_U_int_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_U_int_e\fR" 4
.IX Item "gsl_sf_hyperg_U_int_e"
.ie n .IP """gsl_sf_hyperg_U_int """ 4
.el .IP "\f(CWgsl_sf_hyperg_U_int \fR" 4
.IX Item "gsl_sf_hyperg_U_int "
.ie n .IP """gsl_sf_hyperg_U_int_e10_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_U_int_e10_e\fR" 4
.IX Item "gsl_sf_hyperg_U_int_e10_e"
.ie n .IP """gsl_sf_hyperg_U_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_U_e\fR" 4
.IX Item "gsl_sf_hyperg_U_e"
.ie n .IP """gsl_sf_hyperg_U """ 4
.el .IP "\f(CWgsl_sf_hyperg_U \fR" 4
.IX Item "gsl_sf_hyperg_U "
.ie n .IP """gsl_sf_hyperg_U_e10_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_U_e10_e\fR" 4
.IX Item "gsl_sf_hyperg_U_e10_e"
.ie n .IP """gsl_sf_hyperg_2F1_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_e\fR" 4
.IX Item "gsl_sf_hyperg_2F1_e"
.ie n .IP """gsl_sf_hyperg_2F1 """ 4
.el .IP "\f(CWgsl_sf_hyperg_2F1 \fR" 4
.IX Item "gsl_sf_hyperg_2F1 "
.ie n .IP """gsl_sf_hyperg_2F1_conj_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_conj_e\fR" 4
.IX Item "gsl_sf_hyperg_2F1_conj_e"
.ie n .IP """gsl_sf_hyperg_2F1_conj""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_conj\fR" 4
.IX Item "gsl_sf_hyperg_2F1_conj"
.ie n .IP """gsl_sf_hyperg_2F1_renorm_e """ 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_renorm_e \fR" 4
.IX Item "gsl_sf_hyperg_2F1_renorm_e "
.ie n .IP """gsl_sf_hyperg_2F1_renorm""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_renorm\fR" 4
.IX Item "gsl_sf_hyperg_2F1_renorm"
.ie n .IP """gsl_sf_hyperg_2F1_conj_renorm_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_conj_renorm_e\fR" 4
.IX Item "gsl_sf_hyperg_2F1_conj_renorm_e"
.ie n .IP """gsl_sf_hyperg_2F1_conj_renorm """ 4
.el .IP "\f(CWgsl_sf_hyperg_2F1_conj_renorm \fR" 4
.IX Item "gsl_sf_hyperg_2F1_conj_renorm "
.ie n .IP """gsl_sf_hyperg_2F0_e""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F0_e\fR" 4
.IX Item "gsl_sf_hyperg_2F0_e"
.ie n .IP """gsl_sf_hyperg_2F0""" 4
.el .IP "\f(CWgsl_sf_hyperg_2F0\fR" 4
.IX Item "gsl_sf_hyperg_2F0"
.ie n .IP """gsl_sf_laguerre_1_e """ 4
.el .IP "\f(CWgsl_sf_laguerre_1_e \fR" 4
.IX Item "gsl_sf_laguerre_1_e "
.ie n .IP """gsl_sf_laguerre_2_e""" 4
.el .IP "\f(CWgsl_sf_laguerre_2_e\fR" 4
.IX Item "gsl_sf_laguerre_2_e"
.ie n .IP """gsl_sf_laguerre_3_e""" 4
.el .IP "\f(CWgsl_sf_laguerre_3_e\fR" 4
.IX Item "gsl_sf_laguerre_3_e"
.ie n .IP """gsl_sf_laguerre_1 """ 4
.el .IP "\f(CWgsl_sf_laguerre_1 \fR" 4
.IX Item "gsl_sf_laguerre_1 "
.ie n .IP """gsl_sf_laguerre_2""" 4
.el .IP "\f(CWgsl_sf_laguerre_2\fR" 4
.IX Item "gsl_sf_laguerre_2"
.ie n .IP """gsl_sf_laguerre_3""" 4
.el .IP "\f(CWgsl_sf_laguerre_3\fR" 4
.IX Item "gsl_sf_laguerre_3"
.ie n .IP """gsl_sf_laguerre_n_e """ 4
.el .IP "\f(CWgsl_sf_laguerre_n_e \fR" 4
.IX Item "gsl_sf_laguerre_n_e "
.ie n .IP """gsl_sf_laguerre_n""" 4
.el .IP "\f(CWgsl_sf_laguerre_n\fR" 4
.IX Item "gsl_sf_laguerre_n"
.ie n .IP """gsl_sf_lambert_W0_e""" 4
.el .IP "\f(CWgsl_sf_lambert_W0_e\fR" 4
.IX Item "gsl_sf_lambert_W0_e"
.ie n .IP """gsl_sf_lambert_W0 """ 4
.el .IP "\f(CWgsl_sf_lambert_W0 \fR" 4
.IX Item "gsl_sf_lambert_W0 "
.ie n .IP """gsl_sf_lambert_Wm1_e""" 4
.el .IP "\f(CWgsl_sf_lambert_Wm1_e\fR" 4
.IX Item "gsl_sf_lambert_Wm1_e"
.ie n .IP """gsl_sf_lambert_Wm1""" 4
.el .IP "\f(CWgsl_sf_lambert_Wm1\fR" 4
.IX Item "gsl_sf_lambert_Wm1"
.ie n .IP """gsl_sf_conicalP_half_e """ 4
.el .IP "\f(CWgsl_sf_conicalP_half_e \fR" 4
.IX Item "gsl_sf_conicalP_half_e "
.ie n .IP """gsl_sf_conicalP_half""" 4
.el .IP "\f(CWgsl_sf_conicalP_half\fR" 4
.IX Item "gsl_sf_conicalP_half"
.ie n .IP """gsl_sf_conicalP_mhalf_e""" 4
.el .IP "\f(CWgsl_sf_conicalP_mhalf_e\fR" 4
.IX Item "gsl_sf_conicalP_mhalf_e"
.ie n .IP """gsl_sf_conicalP_mhalf """ 4
.el .IP "\f(CWgsl_sf_conicalP_mhalf \fR" 4
.IX Item "gsl_sf_conicalP_mhalf "
.ie n .IP """gsl_sf_conicalP_0_e""" 4
.el .IP "\f(CWgsl_sf_conicalP_0_e\fR" 4
.IX Item "gsl_sf_conicalP_0_e"
.ie n .IP """gsl_sf_conicalP_0""" 4
.el .IP "\f(CWgsl_sf_conicalP_0\fR" 4
.IX Item "gsl_sf_conicalP_0"
.ie n .IP """gsl_sf_conicalP_1_e """ 4
.el .IP "\f(CWgsl_sf_conicalP_1_e \fR" 4
.IX Item "gsl_sf_conicalP_1_e "
.ie n .IP """gsl_sf_conicalP_1""" 4
.el .IP "\f(CWgsl_sf_conicalP_1\fR" 4
.IX Item "gsl_sf_conicalP_1"
.ie n .IP """gsl_sf_conicalP_sph_reg_e""" 4
.el .IP "\f(CWgsl_sf_conicalP_sph_reg_e\fR" 4
.IX Item "gsl_sf_conicalP_sph_reg_e"
.ie n .IP """gsl_sf_conicalP_sph_reg """ 4
.el .IP "\f(CWgsl_sf_conicalP_sph_reg \fR" 4
.IX Item "gsl_sf_conicalP_sph_reg "
.ie n .IP """gsl_sf_conicalP_cyl_reg_e""" 4
.el .IP "\f(CWgsl_sf_conicalP_cyl_reg_e\fR" 4
.IX Item "gsl_sf_conicalP_cyl_reg_e"
.ie n .IP """gsl_sf_conicalP_cyl_reg""" 4
.el .IP "\f(CWgsl_sf_conicalP_cyl_reg\fR" 4
.IX Item "gsl_sf_conicalP_cyl_reg"
.ie n .IP """gsl_sf_legendre_H3d_0_e """ 4
.el .IP "\f(CWgsl_sf_legendre_H3d_0_e \fR" 4
.IX Item "gsl_sf_legendre_H3d_0_e "
.ie n .IP """gsl_sf_legendre_H3d_0""" 4
.el .IP "\f(CWgsl_sf_legendre_H3d_0\fR" 4
.IX Item "gsl_sf_legendre_H3d_0"
.ie n .IP """gsl_sf_legendre_H3d_1_e""" 4
.el .IP "\f(CWgsl_sf_legendre_H3d_1_e\fR" 4
.IX Item "gsl_sf_legendre_H3d_1_e"
.ie n .IP """gsl_sf_legendre_H3d_1 """ 4
.el .IP "\f(CWgsl_sf_legendre_H3d_1 \fR" 4
.IX Item "gsl_sf_legendre_H3d_1 "
.ie n .IP """gsl_sf_legendre_H3d_e""" 4
.el .IP "\f(CWgsl_sf_legendre_H3d_e\fR" 4
.IX Item "gsl_sf_legendre_H3d_e"
.ie n .IP """gsl_sf_legendre_H3d""" 4
.el .IP "\f(CWgsl_sf_legendre_H3d\fR" 4
.IX Item "gsl_sf_legendre_H3d"
.ie n .IP """gsl_sf_legendre_H3d_array """ 4
.el .IP "\f(CWgsl_sf_legendre_H3d_array \fR" 4
.IX Item "gsl_sf_legendre_H3d_array "
.ie n .IP """gsl_sf_log_e""" 4
.el .IP "\f(CWgsl_sf_log_e\fR" 4
.IX Item "gsl_sf_log_e"
.ie n .IP """gsl_sf_log""" 4
.el .IP "\f(CWgsl_sf_log\fR" 4
.IX Item "gsl_sf_log"
.ie n .IP """gsl_sf_log_abs_e """ 4
.el .IP "\f(CWgsl_sf_log_abs_e \fR" 4
.IX Item "gsl_sf_log_abs_e "
.ie n .IP """gsl_sf_log_abs""" 4
.el .IP "\f(CWgsl_sf_log_abs\fR" 4
.IX Item "gsl_sf_log_abs"
.ie n .IP """gsl_sf_complex_log_e""" 4
.el .IP "\f(CWgsl_sf_complex_log_e\fR" 4
.IX Item "gsl_sf_complex_log_e"
.ie n .IP """gsl_sf_log_1plusx_e """ 4
.el .IP "\f(CWgsl_sf_log_1plusx_e \fR" 4
.IX Item "gsl_sf_log_1plusx_e "
.ie n .IP """gsl_sf_log_1plusx""" 4
.el .IP "\f(CWgsl_sf_log_1plusx\fR" 4
.IX Item "gsl_sf_log_1plusx"
.ie n .IP """gsl_sf_log_1plusx_mx_e""" 4
.el .IP "\f(CWgsl_sf_log_1plusx_mx_e\fR" 4
.IX Item "gsl_sf_log_1plusx_mx_e"
.ie n .IP """gsl_sf_log_1plusx_mx """ 4
.el .IP "\f(CWgsl_sf_log_1plusx_mx \fR" 4
.IX Item "gsl_sf_log_1plusx_mx "
.ie n .IP """gsl_sf_mathieu_a_array""" 4
.el .IP "\f(CWgsl_sf_mathieu_a_array\fR" 4
.IX Item "gsl_sf_mathieu_a_array"
.ie n .IP """gsl_sf_mathieu_b_array""" 4
.el .IP "\f(CWgsl_sf_mathieu_b_array\fR" 4
.IX Item "gsl_sf_mathieu_b_array"
.ie n .IP """gsl_sf_mathieu_a """ 4
.el .IP "\f(CWgsl_sf_mathieu_a \fR" 4
.IX Item "gsl_sf_mathieu_a "
.ie n .IP """gsl_sf_mathieu_b""" 4
.el .IP "\f(CWgsl_sf_mathieu_b\fR" 4
.IX Item "gsl_sf_mathieu_b"
.ie n .IP """gsl_sf_mathieu_a_coeff""" 4
.el .IP "\f(CWgsl_sf_mathieu_a_coeff\fR" 4
.IX Item "gsl_sf_mathieu_a_coeff"
.ie n .IP """gsl_sf_mathieu_b_coeff """ 4
.el .IP "\f(CWgsl_sf_mathieu_b_coeff \fR" 4
.IX Item "gsl_sf_mathieu_b_coeff "
.ie n .IP """gsl_sf_mathieu_alloc""" 4
.el .IP "\f(CWgsl_sf_mathieu_alloc\fR" 4
.IX Item "gsl_sf_mathieu_alloc"
.ie n .IP """gsl_sf_mathieu_free""" 4
.el .IP "\f(CWgsl_sf_mathieu_free\fR" 4
.IX Item "gsl_sf_mathieu_free"
.ie n .IP """gsl_sf_mathieu_ce """ 4
.el .IP "\f(CWgsl_sf_mathieu_ce \fR" 4
.IX Item "gsl_sf_mathieu_ce "
.ie n .IP """gsl_sf_mathieu_se""" 4
.el .IP "\f(CWgsl_sf_mathieu_se\fR" 4
.IX Item "gsl_sf_mathieu_se"
.ie n .IP """gsl_sf_mathieu_ce_array""" 4
.el .IP "\f(CWgsl_sf_mathieu_ce_array\fR" 4
.IX Item "gsl_sf_mathieu_ce_array"
.ie n .IP """gsl_sf_mathieu_se_array """ 4
.el .IP "\f(CWgsl_sf_mathieu_se_array \fR" 4
.IX Item "gsl_sf_mathieu_se_array "
.ie n .IP """gsl_sf_mathieu_Mc""" 4
.el .IP "\f(CWgsl_sf_mathieu_Mc\fR" 4
.IX Item "gsl_sf_mathieu_Mc"
.ie n .IP """gsl_sf_mathieu_Ms""" 4
.el .IP "\f(CWgsl_sf_mathieu_Ms\fR" 4
.IX Item "gsl_sf_mathieu_Ms"
.ie n .IP """gsl_sf_mathieu_Mc_array """ 4
.el .IP "\f(CWgsl_sf_mathieu_Mc_array \fR" 4
.IX Item "gsl_sf_mathieu_Mc_array "
.ie n .IP """gsl_sf_mathieu_Ms_array""" 4
.el .IP "\f(CWgsl_sf_mathieu_Ms_array\fR" 4
.IX Item "gsl_sf_mathieu_Ms_array"
.ie n .IP """gsl_sf_pow_int_e""" 4
.el .IP "\f(CWgsl_sf_pow_int_e\fR" 4
.IX Item "gsl_sf_pow_int_e"
.ie n .IP """gsl_sf_pow_int """ 4
.el .IP "\f(CWgsl_sf_pow_int \fR" 4
.IX Item "gsl_sf_pow_int "
.ie n .IP """gsl_sf_psi_int_e""" 4
.el .IP "\f(CWgsl_sf_psi_int_e\fR" 4
.IX Item "gsl_sf_psi_int_e"
.ie n .IP """gsl_sf_psi_int""" 4
.el .IP "\f(CWgsl_sf_psi_int\fR" 4
.IX Item "gsl_sf_psi_int"
.ie n .IP """gsl_sf_psi_e """ 4
.el .IP "\f(CWgsl_sf_psi_e \fR" 4
.IX Item "gsl_sf_psi_e "
.ie n .IP """gsl_sf_psi""" 4
.el .IP "\f(CWgsl_sf_psi\fR" 4
.IX Item "gsl_sf_psi"
.ie n .IP """gsl_sf_psi_1piy_e""" 4
.el .IP "\f(CWgsl_sf_psi_1piy_e\fR" 4
.IX Item "gsl_sf_psi_1piy_e"
.ie n .IP """gsl_sf_psi_1piy """ 4
.el .IP "\f(CWgsl_sf_psi_1piy \fR" 4
.IX Item "gsl_sf_psi_1piy "
.ie n .IP """gsl_sf_complex_psi_e""" 4
.el .IP "\f(CWgsl_sf_complex_psi_e\fR" 4
.IX Item "gsl_sf_complex_psi_e"
.ie n .IP """gsl_sf_psi_1_int_e""" 4
.el .IP "\f(CWgsl_sf_psi_1_int_e\fR" 4
.IX Item "gsl_sf_psi_1_int_e"
.ie n .IP """gsl_sf_psi_1_int """ 4
.el .IP "\f(CWgsl_sf_psi_1_int \fR" 4
.IX Item "gsl_sf_psi_1_int "
.ie n .IP """gsl_sf_psi_1_e """ 4
.el .IP "\f(CWgsl_sf_psi_1_e \fR" 4
.IX Item "gsl_sf_psi_1_e "
.ie n .IP """gsl_sf_psi_1""" 4
.el .IP "\f(CWgsl_sf_psi_1\fR" 4
.IX Item "gsl_sf_psi_1"
.ie n .IP """gsl_sf_psi_n_e """ 4
.el .IP "\f(CWgsl_sf_psi_n_e \fR" 4
.IX Item "gsl_sf_psi_n_e "
.ie n .IP """gsl_sf_psi_n""" 4
.el .IP "\f(CWgsl_sf_psi_n\fR" 4
.IX Item "gsl_sf_psi_n"
.ie n .IP """gsl_sf_result_smash_e""" 4
.el .IP "\f(CWgsl_sf_result_smash_e\fR" 4
.IX Item "gsl_sf_result_smash_e"
.ie n .IP """gsl_sf_synchrotron_1_e """ 4
.el .IP "\f(CWgsl_sf_synchrotron_1_e \fR" 4
.IX Item "gsl_sf_synchrotron_1_e "
.ie n .IP """gsl_sf_synchrotron_1""" 4
.el .IP "\f(CWgsl_sf_synchrotron_1\fR" 4
.IX Item "gsl_sf_synchrotron_1"
.ie n .IP """gsl_sf_synchrotron_2_e""" 4
.el .IP "\f(CWgsl_sf_synchrotron_2_e\fR" 4
.IX Item "gsl_sf_synchrotron_2_e"
.ie n .IP """gsl_sf_synchrotron_2 """ 4
.el .IP "\f(CWgsl_sf_synchrotron_2 \fR" 4
.IX Item "gsl_sf_synchrotron_2 "
.ie n .IP """gsl_sf_transport_2_e""" 4
.el .IP "\f(CWgsl_sf_transport_2_e\fR" 4
.IX Item "gsl_sf_transport_2_e"
.ie n .IP """gsl_sf_transport_2""" 4
.el .IP "\f(CWgsl_sf_transport_2\fR" 4
.IX Item "gsl_sf_transport_2"
.ie n .IP """gsl_sf_transport_3_e """ 4
.el .IP "\f(CWgsl_sf_transport_3_e \fR" 4
.IX Item "gsl_sf_transport_3_e "
.ie n .IP """gsl_sf_transport_3""" 4
.el .IP "\f(CWgsl_sf_transport_3\fR" 4
.IX Item "gsl_sf_transport_3"
.ie n .IP """gsl_sf_transport_4_e""" 4
.el .IP "\f(CWgsl_sf_transport_4_e\fR" 4
.IX Item "gsl_sf_transport_4_e"
.ie n .IP """gsl_sf_transport_4 """ 4
.el .IP "\f(CWgsl_sf_transport_4 \fR" 4
.IX Item "gsl_sf_transport_4 "
.ie n .IP """gsl_sf_transport_5_e""" 4
.el .IP "\f(CWgsl_sf_transport_5_e\fR" 4
.IX Item "gsl_sf_transport_5_e"
.ie n .IP """gsl_sf_transport_5""" 4
.el .IP "\f(CWgsl_sf_transport_5\fR" 4
.IX Item "gsl_sf_transport_5"
.ie n .IP """gsl_sf_sin_e """ 4
.el .IP "\f(CWgsl_sf_sin_e \fR" 4
.IX Item "gsl_sf_sin_e "
.ie n .IP """gsl_sf_sin""" 4
.el .IP "\f(CWgsl_sf_sin\fR" 4
.IX Item "gsl_sf_sin"
.ie n .IP """gsl_sf_cos_e""" 4
.el .IP "\f(CWgsl_sf_cos_e\fR" 4
.IX Item "gsl_sf_cos_e"
.ie n .IP """gsl_sf_cos """ 4
.el .IP "\f(CWgsl_sf_cos \fR" 4
.IX Item "gsl_sf_cos "
.ie n .IP """gsl_sf_hypot_e""" 4
.el .IP "\f(CWgsl_sf_hypot_e\fR" 4
.IX Item "gsl_sf_hypot_e"
.ie n .IP """gsl_sf_hypot""" 4
.el .IP "\f(CWgsl_sf_hypot\fR" 4
.IX Item "gsl_sf_hypot"
.ie n .IP """gsl_sf_complex_sin_e """ 4
.el .IP "\f(CWgsl_sf_complex_sin_e \fR" 4
.IX Item "gsl_sf_complex_sin_e "
.ie n .IP """gsl_sf_complex_cos_e""" 4
.el .IP "\f(CWgsl_sf_complex_cos_e\fR" 4
.IX Item "gsl_sf_complex_cos_e"
.ie n .IP """gsl_sf_complex_logsin_e""" 4
.el .IP "\f(CWgsl_sf_complex_logsin_e\fR" 4
.IX Item "gsl_sf_complex_logsin_e"
.ie n .IP """gsl_sf_sinc_e """ 4
.el .IP "\f(CWgsl_sf_sinc_e \fR" 4
.IX Item "gsl_sf_sinc_e "
.ie n .IP """gsl_sf_sinc""" 4
.el .IP "\f(CWgsl_sf_sinc\fR" 4
.IX Item "gsl_sf_sinc"
.ie n .IP """gsl_sf_lnsinh_e""" 4
.el .IP "\f(CWgsl_sf_lnsinh_e\fR" 4
.IX Item "gsl_sf_lnsinh_e"
.ie n .IP """gsl_sf_lnsinh """ 4
.el .IP "\f(CWgsl_sf_lnsinh \fR" 4
.IX Item "gsl_sf_lnsinh "
.ie n .IP """gsl_sf_lncosh_e""" 4
.el .IP "\f(CWgsl_sf_lncosh_e\fR" 4
.IX Item "gsl_sf_lncosh_e"
.ie n .IP """gsl_sf_lncosh""" 4
.el .IP "\f(CWgsl_sf_lncosh\fR" 4
.IX Item "gsl_sf_lncosh"
.ie n .IP """gsl_sf_polar_to_rect """ 4
.el .IP "\f(CWgsl_sf_polar_to_rect \fR" 4
.IX Item "gsl_sf_polar_to_rect "
.ie n .IP """gsl_sf_rect_to_polar""" 4
.el .IP "\f(CWgsl_sf_rect_to_polar\fR" 4
.IX Item "gsl_sf_rect_to_polar"
.ie n .IP """gsl_sf_sin_err_e""" 4
.el .IP "\f(CWgsl_sf_sin_err_e\fR" 4
.IX Item "gsl_sf_sin_err_e"
.ie n .IP """gsl_sf_cos_err_e """ 4
.el .IP "\f(CWgsl_sf_cos_err_e \fR" 4
.IX Item "gsl_sf_cos_err_e "
.ie n .IP """gsl_sf_angle_restrict_symm_e""" 4
.el .IP "\f(CWgsl_sf_angle_restrict_symm_e\fR" 4
.IX Item "gsl_sf_angle_restrict_symm_e"
.ie n .IP """gsl_sf_angle_restrict_symm""" 4
.el .IP "\f(CWgsl_sf_angle_restrict_symm\fR" 4
.IX Item "gsl_sf_angle_restrict_symm"
.ie n .IP """gsl_sf_angle_restrict_pos_e """ 4
.el .IP "\f(CWgsl_sf_angle_restrict_pos_e \fR" 4
.IX Item "gsl_sf_angle_restrict_pos_e "
.ie n .IP """gsl_sf_angle_restrict_pos""" 4
.el .IP "\f(CWgsl_sf_angle_restrict_pos\fR" 4
.IX Item "gsl_sf_angle_restrict_pos"
.ie n .IP """gsl_sf_angle_restrict_symm_err_e""" 4
.el .IP "\f(CWgsl_sf_angle_restrict_symm_err_e\fR" 4
.IX Item "gsl_sf_angle_restrict_symm_err_e"
.ie n .IP """gsl_sf_angle_restrict_pos_err_e """ 4
.el .IP "\f(CWgsl_sf_angle_restrict_pos_err_e \fR" 4
.IX Item "gsl_sf_angle_restrict_pos_err_e "
.RS 4
.ie n .IP """gsl_sf_atanint_e""" 4
.el .IP "\f(CWgsl_sf_atanint_e\fR" 4
.IX Item "gsl_sf_atanint_e"
.ie n .IP """gsl_sf_atanint""" 4
.el .IP "\f(CWgsl_sf_atanint\fR" 4
.IX Item "gsl_sf_atanint"
.PD
These routines compute the Arctangent integral, which is defined as AtanInt(x) = \eint_0^x dt \earctan(t)/t.
.RE
.RS 4
.RE
.ie n .IP """gsl_sf_zeta_int_e """ 4
.el .IP "\f(CWgsl_sf_zeta_int_e \fR" 4
.IX Item "gsl_sf_zeta_int_e "
.PD 0
.ie n .IP """gsl_sf_zeta_int""" 4
.el .IP "\f(CWgsl_sf_zeta_int\fR" 4
.IX Item "gsl_sf_zeta_int"
.ie n .IP """gsl_sf_zeta_e gsl_sf_zeta """ 4
.el .IP "\f(CWgsl_sf_zeta_e gsl_sf_zeta \fR" 4
.IX Item "gsl_sf_zeta_e gsl_sf_zeta "
.ie n .IP """gsl_sf_zetam1_e""" 4
.el .IP "\f(CWgsl_sf_zetam1_e\fR" 4
.IX Item "gsl_sf_zetam1_e"
.ie n .IP """gsl_sf_zetam1""" 4
.el .IP "\f(CWgsl_sf_zetam1\fR" 4
.IX Item "gsl_sf_zetam1"
.ie n .IP """gsl_sf_zetam1_int_e """ 4
.el .IP "\f(CWgsl_sf_zetam1_int_e \fR" 4
.IX Item "gsl_sf_zetam1_int_e "
.ie n .IP """gsl_sf_zetam1_int""" 4
.el .IP "\f(CWgsl_sf_zetam1_int\fR" 4
.IX Item "gsl_sf_zetam1_int"
.ie n .IP """gsl_sf_hzeta_e""" 4
.el .IP "\f(CWgsl_sf_hzeta_e\fR" 4
.IX Item "gsl_sf_hzeta_e"
.ie n .IP """gsl_sf_hzeta """ 4
.el .IP "\f(CWgsl_sf_hzeta \fR" 4
.IX Item "gsl_sf_hzeta "
.ie n .IP """gsl_sf_eta_int_e""" 4
.el .IP "\f(CWgsl_sf_eta_int_e\fR" 4
.IX Item "gsl_sf_eta_int_e"
.ie n .IP """gsl_sf_eta_int""" 4
.el .IP "\f(CWgsl_sf_eta_int\fR" 4
.IX Item "gsl_sf_eta_int"
.ie n .IP """gsl_sf_eta_e""" 4
.el .IP "\f(CWgsl_sf_eta_e\fR" 4
.IX Item "gsl_sf_eta_e"
.ie n .IP """gsl_sf_eta """ 4
.el .IP "\f(CWgsl_sf_eta \fR" 4
.IX Item "gsl_sf_eta "
.PD
.PP
This module also contains the following constants used as mode in various of those functions :
.IP "\(bu" 4
\&\s-1GSL_PREC_DOUBLE\s0 \- Double-precision, a relative accuracy of approximately 2 * 10^\-16.
.IP "\(bu" 4
\&\s-1GSL_PREC_SINGLE\s0 \- Single-precision, a relative accuracy of approximately 10^\-7.
.IP "\(bu" 4
\&\s-1GSL_PREC_APPROX\s0 \- Approximate values, a relative accuracy of approximately 5 * 10^\-4.
.PP
.Vb 6
\& You can import the functions that you want to use by giving a space separated
\& list to Math::GSL::SF when you use the package.  You can also write
\& use Math::GSL::SF qw/:all/
\& to use all available functions of the module. Note that
\& the tag names begin with a colon.  Other tags are also available, here is a
\& complete list of all tags for this module :
.Ve
.ie n .IP """airy""" 4
.el .IP "\f(CWairy\fR" 4
.IX Item "airy"
.PD 0
.ie n .IP """bessel""" 4
.el .IP "\f(CWbessel\fR" 4
.IX Item "bessel"
.ie n .IP """clausen""" 4
.el .IP "\f(CWclausen\fR" 4
.IX Item "clausen"
.ie n .IP """hydrogenic""" 4
.el .IP "\f(CWhydrogenic\fR" 4
.IX Item "hydrogenic"
.ie n .IP """coulumb""" 4
.el .IP "\f(CWcoulumb\fR" 4
.IX Item "coulumb"
.ie n .IP """coupling""" 4
.el .IP "\f(CWcoupling\fR" 4
.IX Item "coupling"
.ie n .IP """dawson""" 4
.el .IP "\f(CWdawson\fR" 4
.IX Item "dawson"
.ie n .IP """debye""" 4
.el .IP "\f(CWdebye\fR" 4
.IX Item "debye"
.ie n .IP """dilog""" 4
.el .IP "\f(CWdilog\fR" 4
.IX Item "dilog"
.ie n .IP """factorial""" 4
.el .IP "\f(CWfactorial\fR" 4
.IX Item "factorial"
.ie n .IP """misc""" 4
.el .IP "\f(CWmisc\fR" 4
.IX Item "misc"
.ie n .IP """elliptic""" 4
.el .IP "\f(CWelliptic\fR" 4
.IX Item "elliptic"
.ie n .IP """error""" 4
.el .IP "\f(CWerror\fR" 4
.IX Item "error"
.ie n .IP """hypergeometric""" 4
.el .IP "\f(CWhypergeometric\fR" 4
.IX Item "hypergeometric"
.ie n .IP """laguerre""" 4
.el .IP "\f(CWlaguerre\fR" 4
.IX Item "laguerre"
.ie n .IP """legendre""" 4
.el .IP "\f(CWlegendre\fR" 4
.IX Item "legendre"
.ie n .IP """gamma""" 4
.el .IP "\f(CWgamma\fR" 4
.IX Item "gamma"
.ie n .IP """transport""" 4
.el .IP "\f(CWtransport\fR" 4
.IX Item "transport"
.ie n .IP """trig""" 4
.el .IP "\f(CWtrig\fR" 4
.IX Item "trig"
.ie n .IP """zeta""" 4
.el .IP "\f(CWzeta\fR" 4
.IX Item "zeta"
.ie n .IP """eta""" 4
.el .IP "\f(CWeta\fR" 4
.IX Item "eta"
.ie n .IP """vars""" 4
.el .IP "\f(CWvars\fR" 4
.IX Item "vars"
.PD
.PP
For more information on the functions, we refer you to the \s-1GSL\s0 offcial
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>
.SH "EXAMPLES"
.IX Header "EXAMPLES"
This example computes the dilogarithm of 1/10 :
.PP
.Vb 3
\&    use Math::GSL::SF qw/dilog/;
\&    my $x = gsl_sf_dilog(0.1);
\&    print "gsl_sf_dilog(0.1) = $x\en";
.Ve
.PP
An example using Math::GSL::SF and gnuplot is in the \fBexamples/sf\fR folder of the source code.
.SH "AUTHORS"
.IX Header "AUTHORS"
Jonathan \*(L"Duke\*(R" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2011 Jonathan \*(L"Duke\*(R" Leto and Thierry Moisan
.PP
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.