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

  • Authors:

  • Wenchang Chu

  • Affiliations:

  • Dipartimento di Matematica, Università Degli Studi di Lecce, Lecce-Arnesano, Lecce, Italia

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2005

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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.