Harmonic number identities and Hermite-Padé approximations to the logarithm function

By decomposing rational functions into partial fractions, we will establish several striking harmonic number identities including the hardest challenges discovered recently by Driver et al. [Padé approximations to the logarithm II: identities, recurrences and symbolic computation, Ramanujan J., 2003, to appear]. As application, we construct explicitly the generalized Hermite-Padé approximants to the logarithm and therefore resolve completely this open problem in the general case.