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The Ramanujan Journal

, Volume 27, Issue 3, pp 305–328 | Cite as

A new class of identities involving Cauchy numbers, harmonic numbers and zeta values

  • Bernard Candelpergher
  • Marc-Antoine Coppo
Article

Abstract

Improving an old idea of Hermite, we associate to each natural number k a modified zeta function of order k. The evaluation of the values of these functions F k at positive integers reveals a wide class of identities linking Cauchy numbers, harmonic numbers and zeta values.

Keywords

Cauchy numbers Bell polynomials Harmonic numbers Laplace–Borel transform Mellin transform Zeta values Ramanujan summation Hermite’s formula 

Mathematics Subject Classification (2000)

11B83 11M41 33B15 40G99 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Laboratory Jean Alexandre DieudonnéUniversity of Nice Sophia AntipolisNice Cedex 2France

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