Relative Exponential Functions

Function: double gsl_sf_expm1 (double x)

Function: int gsl_sf_expm1_e (double x, gsl_sf_result * result)

These routines compute the quantity @math{\exp(x)-1} using an algorithm that is accurate for small @math{x}.

Function: double gsl_sf_exprel (double x)

Function: int gsl_sf_exprel_e (double x, gsl_sf_result * 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}.

Function: double gsl_sf_exprel_2 (double x)

Function: int gsl_sf_exprel_2_e (double x, gsl_sf_result * 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}.

Function: double gsl_sf_exprel_n (int n, double x)

Function: int gsl_sf_exprel_n_e (int n, double x, gsl_sf_result * result)

These routines compute the @math{N}-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The @math{N}-relative exponential is given by,