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. © 2005 Elsevier Inc. All rights reserved.
Chu, W. (2005). Harmonic number identities and Hermite-Padé approximations to the logarithm function. Journal of Approximation Theory, 137(1), 42–56. https://doi.org/10.1016/j.jat.2005.07.008