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- Function:
*double***gsl_sf_expm1***(double*`x`) - Function:
*int***gsl_sf_expm1_e***(double*`x`, gsl_sf_result *`result`) These routines compute the quantity

*\exp(x)-1*using an algorithm that is accurate for small*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

*(\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*.

- 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

*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*.

- 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

*N*-relative exponential, which is the`n`-th generalization of the functions`gsl_sf_exprel`

and`gsl_sf_exprel_2`

. 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)