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#### 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). The Pochhammer symbol is also known as the Apell symbol and sometimes written as (a,x). When a and a+x are negative integers or zero, the limiting value of the ratio is returned.

— 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)).

— 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|) with a corresponding error term, and sgn = \sgn((a)_x) where (a)_x = \Gamma(a + x)/\Gamma(a).

— 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).

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