Abstract :
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.
