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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. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

### 7.19.3 Pochhammer Symbol

Function: double gsl_sf_poch (double a, double x)
Function: int gsl_sf_poch_e (double a, double x, gsl_sf_result * result)
These routines compute the Pochhammer symbol (a)_x = \Gamma(a + x)/\Gamma(a), subject to a and a+x not being negative integers or zero. The Pochhammer symbol is also known as the Apell symbol and sometimes written as (a,x).
Function: double gsl_sf_lnpoch (double a, double x)
Function: int gsl_sf_lnpoch_e (double a, double x, gsl_sf_result * result)
These routines compute the logarithm of the Pochhammer symbol, \log((a)_x) = \log(\Gamma(a + x)/\Gamma(a)) for a > 0, a+x > 0.
Function: int gsl_sf_lnpoch_sgn_e (double a, double x, gsl_sf_result * result, double * sgn)
These routines compute the sign of the Pochhammer symbol and the logarithm of its magnitude. The computed parameters are result = \log(|(a)_x|) and sgn = \sgn((a)_x) where (a)_x = \Gamma(a + x)/\Gamma(a), subject to a, a+x not being negative integers or zero.
Function: double gsl_sf_pochrel (double a, double x)
Function: int gsl_sf_pochrel_e (double a, double x, gsl_sf_result * result)
These routines compute the relative Pochhammer symbol ((a)_x - 1)/x where (a)_x = \Gamma(a + x)/\Gamma(a).
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition