The polygamma functions of order n are defined by
\psi^{(n)}(x) = (d/dx)^n \psi(x) = (d/dx)^{n+1} \log(\Gamma(x))
where \psi(x) = \Gamma'(x)/\Gamma(x) is known as the digamma function. These functions are declared in the header file gsl_sf_psi.h.