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[Octave-cvsupdate] SF.net SVN: octave:[7275] trunk/octave-forge/main/gsl/doc
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From: <car...@us...> - 2010-04-28 15:58:50
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Revision: 7275
http://octave.svn.sourceforge.net/octave/?rev=7275&view=rev
Author: carandraug
Date: 2010-04-28 15:58:43 +0000 (Wed, 28 Apr 2010)
Log Message:
-----------
Cleaning duplicated functions in gsl documentation
Added Paths:
-----------
trunk/octave-forge/main/gsl/doc/gsl.doc
trunk/octave-forge/main/gsl/doc/gsl.dvi
trunk/octave-forge/main/gsl/doc/gsl.log
trunk/octave-forge/main/gsl/doc/gsl.pdf
trunk/octave-forge/main/gsl/doc/gsl.ps
trunk/octave-forge/main/gsl/doc/gsl.texi
Removed Paths:
-------------
trunk/octave-forge/main/gsl/doc/gsl_sf.cc
trunk/octave-forge/main/gsl/doc/gsl_sf.doc
trunk/octave-forge/main/gsl/doc/gsl_sf.dvi
trunk/octave-forge/main/gsl/doc/gsl_sf.log
trunk/octave-forge/main/gsl/doc/gsl_sf.pdf
trunk/octave-forge/main/gsl/doc/gsl_sf.ps
trunk/octave-forge/main/gsl/doc/gsl_sf.texi
trunk/octave-forge/main/gsl/doc/gsl_sf_a.ps
Copied: trunk/octave-forge/main/gsl/doc/gsl.doc (from rev 7274, trunk/octave-forge/main/gsl/doc/gsl_sf.doc)
===================================================================
--- trunk/octave-forge/main/gsl/doc/gsl.doc (rev 0)
+++ trunk/octave-forge/main/gsl/doc/gsl.doc 2010-04-28 15:58:43 UTC (rev 7275)
@@ -0,0 +1,3830 @@
+ gsl_sf
+-*- texinfo -*-
+@deftypefn {Loadable Function} {} gsl_sf ()
+
+Octave bindings to the GNU Scientific Library. All GSL functions can be
+called with by the GSL names within octave.
+@end deftypefn
+
+ clausen
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} clausen (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} clausen (@dots{})
+
+The Clausen function is defined by the following integral,
+
+Cl_2(x) = - \\int_0^x dt \\log(2 \\sin(t/2))
+
+It is related to the dilogarithm by Cl_2(\\theta) = \\Im Li_2(\\exp(i \\theta)).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ dawson
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} dawson (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} dawson (@dots{})
+
+The Dawson integral is defined by \\exp(-x^2) \\int_0^x dt \\exp(t^2).
+A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ debye_1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} debye_1 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_1 (@dots{})
+
+The Debye functions are defined by the integral
+
+D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).
+
+For further information see Abramowitz & Stegun, Section 27.1.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ debye_2
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} debye_2 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_2 (@dots{})
+
+The Debye functions are defined by the integral
+
+D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).
+
+For further information see Abramowitz & Stegun, Section 27.1.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ debye_3
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} debye_3 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_3 (@dots{})
+
+The Debye functions are defined by the integral
+
+D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).
+
+For further information see Abramowitz & Stegun, Section 27.1.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ debye_4
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} debye_4 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} debye_4 (@dots{})
+
+The Debye functions are defined by the integral
+
+D_n(x) = n/x^n \\int_0^x dt (t^n/(e^t - 1)).
+
+For further information see Abramowitz & Stegun, Section 27.1.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ erf_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} erf_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_gsl (@dots{})
+
+These routines compute the error function
+erf(x) = (2/\\sqrt(\\pi)) \\int_0^x dt \\exp(-t^2).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ erfc_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} erfc_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erfc_gsl (@dots{})
+
+These routines compute the complementary error function
+erfc(x) = 1 - erf(x) = (2/\\sqrt(\\pi)) \\int_x^\\infty \\exp(-t^2).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ log_erfc
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} log_erfc (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_erfc (@dots{})
+
+These routines compute the logarithm of the complementary error
+function \\log(\\erfc(x)).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ erf_Z
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} erf_Z (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Z (@dots{})
+
+These routines compute the Gaussian probability function
+Z(x) = (1/(2\\pi)) \\exp(-x^2/2).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ erf_Q
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} erf_Q (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} erf_Q (@dots{})
+
+These routines compute the upper tail of the Gaussian probability
+function Q(x) = (1/(2\\pi)) \\int_x^\\infty dt \\exp(-t^2/2).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ hazard
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} hazard (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} hazard (@dots{})
+
+The hazard function for the normal distrbution, also known as the
+inverse Mill\\'s ratio, is defined as
+h(x) = Z(x)/Q(x) = \\sqrt@{2/\\pi \\exp(-x^2 / 2) / \\erfc(x/\\sqrt 2)@}.
+It decreases rapidly as x approaches -\\infty and asymptotes to
+h(x) \\sim x as x approaches +\\infty.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ expm1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} expm1 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expm1 (@dots{})
+
+These routines compute the quantity \\exp(x)-1 using an algorithm that
+is accurate for small x.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ exprel
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} exprel (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel (@dots{})
+
+These routines compute the quantity (\\exp(x)-1)/x using an algorithm
+that is accurate for small x. For small x the algorithm is based on
+the expansion (\\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \\dots.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ exprel_2
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} exprel_2 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_2 (@dots{})
+
+These routines compute the quantity 2(\\exp(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(\\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \\dots.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ expint_E1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} expint_E1 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E1 (@dots{})
+
+These routines compute the exponential integral E_1(x),
+
+E_1(x) := Re \\int_1^\\infty dt \\exp(-xt)/t.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ expint_E2
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} expint_E2 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_E2 (@dots{})
+
+These routines compute the second-order exponential integral E_2(x),
+
+E_2(x) := \\Re \\int_1^\\infty dt \\exp(-xt)/t^2.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ expint_Ei
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} expint_Ei (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_Ei (@dots{})
+
+These routines compute the exponential integral E_i(x),
+
+Ei(x) := - PV(\\int_@{-x@}^\\infty dt \\exp(-t)/t)
+
+where PV denotes the principal value of the integral.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ Shi
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} Shi (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Shi (@dots{})
+
+These routines compute the integral Shi(x) = \\int_0^x dt \\sinh(t)/t.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ Chi
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} Chi (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Chi (@dots{})
+
+These routines compute the integral
+
+Chi(x) := Re[ \\gamma_E + \\log(x) + \\int_0^x dt (\\cosh[t]-1)/t] ,
+
+where \\gamma_E is the Euler constant.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ expint_3
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} expint_3 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} expint_3 (@dots{})
+
+These routines compute the exponential integral
+Ei_3(x) = \\int_0^x dt \\exp(-t^3) for x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ Si
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} Si (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Si (@dots{})
+
+These routines compute the Sine integral Si(x) = \\int_0^x dt \\sin(t)/t.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ Ci
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} Ci (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} Ci (@dots{})
+
+These routines compute the Cosine integral
+Ci(x) = -\\int_x^\\infty dt \\cos(t)/t for x > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ atanint
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} atanint (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} atanint (@dots{})
+
+These routines compute the Arctangent integral
+AtanInt(x) = \\int_0^x dt \\arctan(t)/t.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ fermi_dirac_mhalf
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} fermi_dirac_mhalf (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_mhalf (@dots{})
+
+These routines compute the complete Fermi-Dirac integral F_@{-1/2@}(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ fermi_dirac_half
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} fermi_dirac_half (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_half (@dots{})
+
+These routines compute the complete Fermi-Dirac integral F_@{1/2@}(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ fermi_dirac_3half
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} fermi_dirac_3half (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_3half (@dots{})
+
+These routines compute the complete Fermi-Dirac integral F_@{3/2@}(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gamma_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} gamma_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gamma_gsl (@dots{})
+
+These routines compute the Gamma function \\Gamma(x), subject to x not
+being a negative integer. The function is computed using the real
+Lanczos method. The maximum value of x such that \\Gamma(x) is not
+considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lngamma_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} lngamma_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lngamma_gsl (@dots{})
+
+These routines compute the logarithm of the Gamma function,
+\\log(\\Gamma(x)), subject to x not a being negative integer.
+For x<0 the real part of \\log(\\Gamma(x)) is returned, which is
+equivalent to \\log(|\\Gamma(x)|). The function is computed using
+the real Lanczos method.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gammastar
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} gammastar (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammastar (@dots{})
+
+These routines compute the regulated Gamma Function \\Gamma^*(x)
+for x > 0. The regulated gamma function is given by,
+
+\\Gamma^*(x) = \\Gamma(x)/(\\sqrt@{2\\pi@} x^@{(x-1/2)@} \\exp(-x))
+ = (1 + (1/12x) + ...) for x \\to \\infty
+
+and is a useful suggestion of Temme.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gammainv_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} gammainv_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} gammainv_gsl (@dots{})
+
+These routines compute the reciprocal of the gamma function, 1/\\Gamma(x) using the real Lanczos method.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lambert_W0
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} lambert_W0 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_W0 (@dots{})
+
+These compute the principal branch of the Lambert W function, W_0(x).
+
+Lambert\\'s W functions, W(x), are defined to be solutions of the
+equation W(x) \\exp(W(x)) = x. This function has multiple branches
+for x < 0; however, it has only two real-valued branches.
+We define W_0(x) to be the principal branch, where W > -1 for x < 0,
+and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lambert_Wm1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} lambert_Wm1 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lambert_Wm1 (@dots{})
+
+These compute the secondary real-valued branch of the Lambert
+W function, W_@{-1@}(x).
+
+Lambert\\'s W functions, W(x), are defined to be solutions of the
+equation W(x) \\exp(W(x)) = x. This function has multiple branches
+for x < 0; however, it has only two real-valued branches.
+We define W_0(x) to be the principal branch, where W > -1 for x < 0,
+and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ log_1plusx
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} log_1plusx (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx (@dots{})
+
+These routines compute \\log(1 + x) for x > -1 using an algorithm that
+is accurate for small x.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ log_1plusx_mx
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} log_1plusx_mx (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} log_1plusx_mx (@dots{})
+
+These routines compute \\log(1 + x) - x for x > -1 using an algorithm
+that is accurate for small x.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ psi
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} psi (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi (@dots{})
+
+These routines compute the digamma function \\psi(x) for general x,
+x \
+e 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ psi_1piy
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} psi_1piy (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_1piy (@dots{})
+
+These routines compute the real part of the digamma function on
+the line 1+i y, Re[\\psi(1 + i y)].
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ synchrotron_1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} synchrotron_1 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_1 (@dots{})
+
+These routines compute the first synchrotron function
+x \\int_x^\\infty dt K_@{5/3@}(t) for x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ synchrotron_2
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} synchrotron_2 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} synchrotron_2 (@dots{})
+
+These routines compute the second synchrotron function
+x K_@{2/3@}(x) for x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ transport_2
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} transport_2 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_2 (@dots{})
+
+These routines compute the transport function J(2,x).
+
+The transport functions J(n,x) are defined by the integral
+representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ transport_3
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} transport_3 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_3 (@dots{})
+
+These routines compute the transport function J(3,x).
+
+The transport functions J(n,x) are defined by the integral
+representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ transport_4
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} transport_4 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_4 (@dots{})
+
+These routines compute the transport function J(4,x).
+
+The transport functions J(n,x) are defined by the integral
+representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ transport_5
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} transport_5 (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} transport_5 (@dots{})
+
+These routines compute the transport function J(5,x).
+
+The transport functions J(n,x) are defined by the integral
+representations J(n,x) := \\int_0^x dt t^n e^t /(e^t - 1)^2.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ sinc_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} sinc_gsl (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} sinc_gsl (@dots{})
+
+These routines compute \\sinc(x) = \\sin(\\pi x) / (\\pi x) for any value of x.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lnsinh
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} lnsinh (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lnsinh (@dots{})
+
+These routines compute \\log(\\sinh(x)) for x > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lncosh
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} lncosh (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} lncosh (@dots{})
+
+These routines compute \\log(\\cosh(x)) for any x.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ zeta
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} zeta (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} zeta (@dots{})
+
+These routines compute the Riemann zeta function \\zeta(s) for
+arbitrary s, s \
+e 1.
+
+The Riemann zeta function is defined by the infinite sum
+\\zeta(s) = \\sum_@{k=1@}^\\infty k^@{-s@}.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ eta
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} eta (@var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} eta (@dots{})
+
+These routines compute the eta function \\eta(s) for arbitrary s.
+
+The eta function is defined by \\eta(s) = (1-2^@{1-s@}) \\zeta(s).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Jn
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_Jn (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Jn (@dots{})
+
+These routines compute the regular cylindrical Bessel function of
+order n, J_n(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Yn
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_Yn (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Yn (@dots{})
+
+These routines compute the irregular cylindrical Bessel function of
+order n, Y_n(x), for x>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_In
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_In (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In (@dots{})
+
+These routines compute the regular modified cylindrical Bessel
+function of order n, I_n(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_In_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_In_scaled (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_In_scaled (@dots{})
+
+These routines compute the scaled regular modified cylindrical Bessel
+function of order n, \\exp(-|x|) I_n(x)
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Kn
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_Kn (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn (@dots{})
+
+These routines compute the irregular modified cylindrical Bessel
+function of order n, K_n(x), for x > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Kn_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_Kn_scaled (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_Kn_scaled (@dots{})
+
+
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_jl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_jl (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_jl (@dots{})
+
+These routines compute the regular spherical Bessel function of
+order l, j_l(x), for l >= 0 and x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_yl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_yl (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_yl (@dots{})
+
+These routines compute the irregular spherical Bessel function of
+order l, y_l(x), for l >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_il_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_il_scaled (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_il_scaled (@dots{})
+
+These routines compute the scaled regular modified spherical Bessel
+function of order l, \\exp(-|x|) i_l(x)
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_kl_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} bessel_kl_scaled (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} bessel_kl_scaled (@dots{})
+
+These routines compute the scaled irregular modified spherical Bessel
+function of order l, \\exp(x) k_l(x), for x>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ exprel_n
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} exprel_n (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} exprel_n (@dots{})
+
+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 (\\exp(x) - \\sum_@{k=0@}^@{N-1@} x^k/k!)
+ = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ...
+ = 1F1 (1,1+N,x)
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ fermi_dirac_int
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} fermi_dirac_int (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} fermi_dirac_int (@dots{})
+
+These routines compute the complete Fermi-Dirac integral with an
+integer index of j, F_j(x) = (1/\\Gamma(j+1)) \\int_0^\\infty dt (t^j
+/(\\exp(t-x)+1)).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ taylorcoeff
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} taylorcoeff (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} taylorcoeff (@dots{})
+
+These routines compute the Taylor coefficient x^n / n!
+for x >= 0, n >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ legendre_Pl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} legendre_Pl (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Pl (@dots{})
+
+These functions evaluate the Legendre polynomial P_l(x) for a specific
+value of l, x subject to l >= 0, |x| <= 1
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ legendre_Ql
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} legendre_Ql (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} legendre_Ql (@dots{})
+
+These routines compute the Legendre function Q_l(x) for x > -1, x != 1
+and l >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ psi_n
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} psi_n (@var{n}, @var{x})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} psi_n (@dots{})
+
+These routines compute the polygamma function \\psi^@{(m)@}(x)
+for m >= 0, x > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Jnu
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Jnu (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Jnu (@dots{})
+
+These routines compute the regular cylindrical Bessel function of
+fractional order nu, J_\
+u(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Ynu
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Ynu (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Ynu (@dots{})
+
+These routines compute the irregular cylindrical Bessel function of
+fractional order nu, Y_\
+u(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Inu
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Inu (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu (@dots{})
+
+These routines compute the regular modified Bessel function of
+fractional order nu, I_\
+u(x) for x>0, \
+u>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Inu_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Inu_scaled (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Inu_scaled (@dots{})
+
+These routines compute the scaled regular modified Bessel function of
+fractional order nu, \\exp(-|x|)I_\
+u(x) for x>0, \
+u>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Knu
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Knu (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu (@dots{})
+
+These routines compute the irregular modified Bessel function of
+fractional order nu, K_\
+u(x) for x>0, \
+u>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_lnKnu
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_lnKnu (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_lnKnu (@dots{})
+
+These routines compute the logarithm of the irregular modified Bessel
+function of fractional order nu, \\ln(K_\
+u(x)) for x>0, \
+u>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ bessel_Knu_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} bessel_Knu_scaled (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} bessel_Knu_scaled (@dots{})
+
+These routines compute the scaled irregular modified Bessel function
+of fractional order nu, \\exp(+|x|) K_\
+u(x) for x>0, \
+u>0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ exp_mult
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} exp_mult (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} exp_mult (@dots{})
+
+These routines exponentiate x and multiply by the factor y to return
+the product y \\exp(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ fermi_dirac_inc_0
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} fermi_dirac_inc_0 (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} fermi_dirac_inc_0 (@dots{})
+
+These routines compute the incomplete Fermi-Dirac integral with an
+index of zero, F_0(x,b) = \\ln(1 + e^@{b-x@}) - (b-x).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ poch
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} poch (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} poch (@dots{})
+
+These routines compute the Pochhammer symbol
+
+(a)_x := \\Gamma(a + x)/\\Gamma(a),
+
+subject to a and a+x not being negative integers. The Pochhammer
+symbol is also known as the Apell symbol.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lnpoch
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} lnpoch (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnpoch (@dots{})
+
+These routines compute the logarithm of the Pochhammer symbol,
+\\log((a)_x) = \\log(\\Gamma(a + x)/\\Gamma(a)) for a > 0, a+x > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ pochrel
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} pochrel (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} pochrel (@dots{})
+
+These routines compute the relative Pochhammer symbol ((a,x) - 1)/x
+where (a,x) = (a)_x := \\Gamma(a + x)/\\Gamma(a).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gamma_inc_Q
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} gamma_inc_Q (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_Q (@dots{})
+
+These routines compute the normalized incomplete Gamma Function
+Q(a,x) = 1/\\Gamma(a) \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a > 0, x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gamma_inc_P
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} gamma_inc_P (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc_P (@dots{})
+
+These routines compute the complementary normalized incomplete Gamma
+Function P(a,x) = 1/\\Gamma(a) \\int_0^x dt t^@{a-1@} \\exp(-t)
+for a > 0, x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ gamma_inc
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} gamma_inc (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} gamma_inc (@dots{})
+
+These functions compute the incomplete Gamma Function the
+normalization factor included in the previously defined functions:
+\\Gamma(a,x) = \\int_x\\infty dt t^@{a-1@} \\exp(-t) for a real and x >= 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ beta_gsl
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} beta_gsl (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} beta_gsl (@dots{})
+
+These routines compute the Beta Function,
+B(a,b) = \\Gamma(a)\\Gamma(b)/\\Gamma(a+b) for a > 0, b > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ lnbeta
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} lnbeta (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} lnbeta (@dots{})
+
+These routines compute the logarithm of the Beta Function,
+\\log(B(a,b)) for a > 0, b > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ hyperg_0F1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} hyperg_0F1 (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hyperg_0F1 (@dots{})
+
+These routines compute the hypergeometric function 0F1(c,x).
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ conicalP_half
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} conicalP_half (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_half (@dots{})
+
+These routines compute the irregular Spherical Conical Function
+P^@{1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ conicalP_mhalf
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} conicalP_mhalf (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_mhalf (@dots{})
+
+These routines compute the regular Spherical Conical Function
+P^@{-1/2@}_@{-1/2 + i \\lambda@}(x) for x > -1.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ conicalP_0
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} conicalP_0 (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_0 (@dots{})
+
+These routines compute the conical function P^0_@{-1/2 + i \\lambda@}(x)
+for x > -1.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ conicalP_1
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} conicalP_1 (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} conicalP_1 (@dots{})
+
+These routines compute the conical function P^1_@{-1/2 + i \\lambda@}(x)
+for x > -1.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ hzeta
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{z} =} hzeta (@var{x}, @var{y})
+@deftypefnx {Loadable Function} {[@var{z}, @var{err}] =} hzeta (@dots{})
+
+These routines compute the Hurwitz zeta function \\zeta(s,q)
+for s > 1, q > 0.
+
+@var{err} contains an estimate of the absolute error in the value @var{z}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Ai
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Ai (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai (@dots{})
+
+These routines compute the Airy function Ai(x) with an accuracy
+specified by mode.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Bi
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Bi (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi (@dots{})
+
+These routines compute the Airy function Bi(x) with an accuracy
+specified by mode.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Ai_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Ai_scaled (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_scaled (@dots{})
+
+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 \\exp(+(2/3) x^(3/2)), and
+is 1 for x<0.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Bi_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Bi_scaled (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_scaled (@dots{})
+
+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.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Ai_deriv
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv (@dots{})
+
+These routines compute the Airy function derivative Ai'(x) with an
+accuracy specified by mode.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Bi_deriv
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv (@dots{})
+
+These routines compute the Airy function derivative Bi'(x) with an
+accuracy specified by mode.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Ai_deriv_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Ai_deriv_scaled (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Ai_deriv_scaled (@dots{})
+
+These routines compute the derivative of the scaled Airy function
+S_A(x) Ai(x).
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_Bi_deriv_scaled
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_Bi_deriv_scaled (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_Bi_deriv_scaled (@dots{})
+
+These routines compute the derivative of the scaled Airy function
+S_B(x) Bi(x).
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ ellint_Kcomp
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} ellint_Kcomp (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Kcomp (@dots{})
+
+These routines compute the complete elliptic integral K(k)
+@tex
+\\beforedisplay
+$$
+\\eqalign{
+K(k) &= \\int_0^{\\pi/2} {dt \\over \\sqrt{(1 - k^2 \\sin^2(t))}} \\cr
+}
+$$
+\\afterdisplay
+See also:
+@end tex
+@ifinfo
+@group
+@example
+ pi
+ ---
+ 2
+ /
+ | 1
+ ellint_Kcomp(k) = | ------------------- dt
+ | 2 2
+ / sqrt(1 - k sin (t))
+ 0
+
+@end example
+@end group
+@end ifinfo
+@ifhtml
+@group
+@example
+ pi
+ ---
+ 2
+ /
+ | 1
+ ellint_Kcomp(k) = | ------------------- dt
+ | 2 2
+ / sqrt(1 - k sin (t))
+ 0
+
+@end example
+@end group
+@end ifhtml
+
+@seealso{ellipj, ellipke}
+
+The notation used here is based on Carlson, @cite{Numerische
+Mathematik} 33 (1979) and differs slightly from that used by
+Abramowitz & Stegun, where the functions are given in terms of the
+parameter @math{m = k^2}.
+
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ ellint_Ecomp
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} ellint_Ecomp (@var{x}, @var{mode})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} ellint_Ecomp (@dots{})
+
+These routines compute the complete elliptic integral E(k) to the
+accuracy specified by the mode variable mode.
+
+@tex
+\\beforedisplay
+$$
+\\eqalign{
+E(k) &= \\int_0^{\\pi/2} \\sqrt{(1 - k^2 \\sin^2(t))} dt \\cr
+}
+$$
+\\afterdisplay
+See also:
+
+@end tex
+@ifinfo
+@group
+@example
+ pi
+ ---
+ 2
+ /
+ | 2 2
+ ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt
+ |
+ /
+ 0
+
+@end example
+@end group
+@end ifinfo
+@ifhtml
+@group
+@example
+ pi
+ ---
+ 2
+ /
+ | 2 2
+ ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt
+ |
+ /
+ 0
+
+@end example
+@end group
+@end ifhtml
+
+@seealso{ellipj, ellipke}
+
+The notation used here is based on Carlson, @cite{Numerische
+Mathematik} 33 (1979) and differs slightly from that used by
+Abramowitz & Stegun, where the functions are given in terms of the
+parameter @math{m = k^2}.
+
+The second argument @var{mode} must be an integer corresponding to
+
+@table @asis
+@item 0 = GSL_PREC_DOUBLE
+ Double-precision, a relative accuracy of approximately @code{2 * 10^-16}.
+@item 1 = GSL_PREC_SINGLE
+ Single-precision, a relative accuracy of approximately @code{10^-7}.
+@item 2 = GSL_PREC_APPROX
+ Approximate values, a relative accuracy of approximately @code{5 * 10^-4}.
+@end table
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_zero_Ai
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai (@var{n})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai (@dots{})
+
+These routines compute the location of the s-th zero of the Airy
+function Ai(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_zero_Bi
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_zero_Bi (@var{n})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Bi (@dots{})
+
+These routines compute the location of the s-th zero of the Airy
+function Bi(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for documentation.
+@end deftypefn
+
+
+ airy_zero_Ai_deriv
+ -*- texinfo -*-
+@deftypefn {Loadable Function} {@var{y} =} airy_zero_Ai_deriv (@var{n})
+@deftypefnx {Loadable Function} {[@var{y}, @var{err}] =} airy_zero_Ai_deriv (@dots{})
+
+These routines compute the location of the s-th zero of the Airy
+function derivative Ai(x).
+
+@var{err} contains an estimate of the absolute error in the value @var{y}.
+
+This function is from the GNU Scientific Library,
+see @url{http://www.gnu.org/software/gsl/} for docu...
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