— Function: double gsl_sf_psi_int (int n)
— Function: int gsl_sf_psi_int_e (int n, gsl_sf_result * result)

These routines compute the digamma function \psi(n) for positive integer n. The digamma function is also called the Psi function.

— Function: double gsl_sf_psi (double x)
— Function: int gsl_sf_psi_e (double x, gsl_sf_result * result)

These routines compute the digamma function \psi(x) for general x, x \ne 0.

— Function: double gsl_sf_psi_1piy (double y)
— Function: int gsl_sf_psi_1piy_e (double y, gsl_sf_result * result)

These routines compute the real part of the digamma function on the line 1+i y, \Re[\psi(1 + i y)].