A generalization of the polylogarithm function defined by S_(n, p)(z) = (-1)^(n + p - 1)/((n - 1)!p!) integral_0^1 ((ln t)^(n - 1) [ln(1 - z t)]^p)/t d t. The function reduces to the usual polylogarithm for the case S_(n - 1, 1)(z) = Li_n(z). The Nielsen generalized polylogarithm is implemented as PolyLog[n, p, z].