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The polygamma functions of order m are defined by
\psi^{(m)}(x) = (d/dx)^m \psi(x) = (d/dx)^{m+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.