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+@cindex exponential function
+@cindex exp
+
+The functions described in this section are declared in the header file
+@file{gsl_sf_exp.h}.
+
+@menu
+* Exponential Function::        
+* Relative Exponential Functions::  
+* Exponentiation With Error Estimate::  
+@end menu
+
+@node Exponential Function
+@subsection Exponential Function
+
+@deftypefun double gsl_sf_exp (double @var{x})
+@deftypefunx int gsl_sf_exp_e (double @var{x}, gsl_sf_result * @var{result})
+These routines provide an exponential function @math{\exp(x)} using GSL
+semantics and error checking.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+
+@deftypefun int gsl_sf_exp_e10_e (double @var{x}, gsl_sf_result_e10 * @var{result})
+This function computes the exponential @math{\exp(x)} using the
+@code{gsl_sf_result_e10} type to return a result with extended range.
+This function may be useful if the value of @math{\exp(x)} would
+overflow the  numeric range of @code{double}.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+
+@deftypefun double gsl_sf_exp_mult (double @var{x}, double @var{y})
+@deftypefunx int gsl_sf_exp_mult_e (double @var{x}, double @var{y}, gsl_sf_result * @var{result})
+These routines exponentiate @var{x} and multiply by the factor @var{y}
+to return the product @math{y \exp(x)}.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+
+@deftypefun int gsl_sf_exp_mult_e10_e (const double @var{x}, const double @var{y}, gsl_sf_result_e10 * @var{result})
+This function computes the product @math{y \exp(x)} using the
+@code{gsl_sf_result_e10} type to return a result with extended numeric
+range.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+
+
+
+@node Relative Exponential Functions
+@subsection Relative Exponential Functions
+
+@deftypefun double gsl_sf_expm1 (double @var{x})
+@deftypefunx int gsl_sf_expm1_e (double @var{x}, gsl_sf_result * @var{result})
+These routines compute the quantity @math{\exp(x)-1} using an algorithm
+that is accurate for small @math{x}.
+@comment Exceptional Return Values:  GSL_EOVRFLW
+@end deftypefun
+
+@deftypefun double gsl_sf_exprel (double @var{x})
+@deftypefunx int gsl_sf_exprel_e (double @var{x}, gsl_sf_result * @var{result})
+These routines compute the quantity @math{(\exp(x)-1)/x} using an
+algorithm that is accurate for small @math{x}.  For small @math{x} the
+algorithm is based on the expansion @math{(\exp(x)-1)/x = 1 + x/2 +
+x^2/(2*3) + x^3/(2*3*4) + \dots}.
+@comment Exceptional Return Values:  GSL_EOVRFLW
+@end deftypefun
+
+@deftypefun double gsl_sf_exprel_2 (double @var{x})
+@deftypefunx int gsl_sf_exprel_2_e (double @var{x}, gsl_sf_result * @var{result})
+These routines compute the quantity @math{2(\exp(x)-1-x)/x^2} using an
+algorithm that is accurate for small @math{x}.  For small @math{x} the
+algorithm is based on the expansion @math{2(\exp(x)-1-x)/x^2 = 
+1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \dots}.
+@comment Exceptional Return Values:  GSL_EOVRFLW
+@end deftypefun
+
+@deftypefun double gsl_sf_exprel_n (int @var{n}, double @var{x})
+@deftypefunx int gsl_sf_exprel_n_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
+These routines compute the @math{N}-relative exponential, which is the
+@var{n}-th generalization of the functions @code{gsl_sf_exprel} and
+@code{gsl_sf_exprel2}.  The @math{N}-relative exponential is given by,
+@tex
+\beforedisplay
+$$
+\eqalign{
+\hbox{exprel}_N(x)
+            &= N!/x^N \left(\exp(x) - \sum_{k=0}^{N-1} x^k/k!\right)\cr
+            &= 1 + x/(N+1) + x^2/((N+1)(N+2)) + \dots\cr
+            &= {}_1F_1(1,1+N,x)\cr
+}
+$$
+\afterdisplay
+@end tex
+@ifinfo
+
+@example
+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)
+@end example
+@end ifinfo
+@comment Exceptional Return Values: 
+@end deftypefun
+
+
+
+@node Exponentiation With Error Estimate
+@subsection Exponentiation With Error Estimate
+
+
+@deftypefun int gsl_sf_exp_err_e (double @var{x}, double @var{dx}, gsl_sf_result * @var{result})
+This function exponentiates @var{x} with an associated absolute error
+@var{dx}.
+@comment Exceptional Return Values: 
+@end deftypefun
+
+@deftypefun int gsl_sf_exp_err_e10_e (double @var{x}, double @var{dx}, gsl_sf_result_e10 * @var{result})
+This function exponentiates a quantity @var{x} with an associated absolute 
+error @var{dx} using the @code{gsl_sf_result_e10} type to return a result with
+extended range.
+@comment Exceptional Return Values: 
+@end deftypefun
+
+@deftypefun int gsl_sf_exp_mult_err_e (double @var{x}, double @var{dx}, double @var{y}, double @var{dy}, gsl_sf_result * @var{result})
+This routine computes the product @math{y \exp(x)} for the quantities
+@var{x}, @var{y} with associated absolute errors @var{dx}, @var{dy}.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+
+
+@deftypefun int gsl_sf_exp_mult_err_e10_e (double @var{x}, double @var{dx}, double @var{y}, double @var{dy}, gsl_sf_result_e10 * @var{result})
+This routine computes the product @math{y \exp(x)} for the quantities
+@var{x}, @var{y} with associated absolute errors @var{dx}, @var{dy} using the
+@code{gsl_sf_result_e10} type to return a result with extended range.
+@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
+@end deftypefun
+