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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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7.16.2 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 \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_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)
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition