Harmonic number identities and Hermite-Pade 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. [Pade approximations to the logarithm II: identities, recurrences and symbolic computation, Ramanujan J., 2003, to appear]. As application, we construct explicitly the generalized Hermite-Pade approximants to the logarithm and therefore resolve completely this open problem in the general case. (c) 2005 Elsevier Inc. All fights reserved.