Psi (Digamma) Function
======================

The poly-gamma functions are defined by psi(m,x) = (d/dx)^m psi(0,x) = (d/dx)^(m+1) log(gamma(x)) , where  \psi(0,x)  is called the di-gamma function.

Digamma Function
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 -- Function: int gsl_sf_psi_int_impl (int n, gsl_sf_result * result)
 -- Function: int gsl_sf_psi_int_e (int n, gsl_sf_result * result)
     Domain: n integer, n > 0 Exceptional Return Values: GSL_EDOM

 -- Function: int gsl_sf_psi_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_psi_e (double x, gsl_sf_result * result)
     Domain: x != 0.0 Exceptional Return Values: GSL_EDOM, GSL_ELOSS

/* Di-Gamma Function Re[psi(1 + I y)] * * exceptions: none */
 -- Function: int gsl_sf_psi_1piy_impl (double y, gsl_sf_result * result)
 -- Function: int gsl_sf_psi_1piy_e (double y, gsl_sf_result * result)
     Computes  Re psi(1 + I y) . Exceptional Return Values: none

Trigamma Function
-----------------

 -- Function: int gsl_sf_psi_1_int_impl (int n, gsl_sf_result * result)
 -- Function: int gsl_sf_psi_1_int_e (int n, gsl_sf_result * result)
     Domain: n integer, n > 0 Exceptional Return Values: GSL_EDOM

Polygamma Function
------------------

 -- Function: int gsl_sf_psi_n_impl (int m, double x, gsl_sf_result * result)
 -- Function: int gsl_sf_psi_n_e (int m, double x, gsl_sf_result * result)
     Domain: m >= 0, x > 0.0 Exceptional Return Values: GSL_EDOM