## File: Pochhammer-Symbol.html

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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114` `````` GNU Scientific Library – Reference Manual: Pochhammer Symbol

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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