Concrete Math
Riordan arrays and harmonic number identities
Computers & Mathematics with Applications
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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.