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Journal Articles Ramanujan Journal (The) Year : 2012

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

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.
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Dates and versions

hal-00495767 , version 1 (28-06-2010)
hal-00495767 , version 2 (30-06-2010)
hal-00495767 , version 3 (15-07-2010)
hal-00495767 , version 4 (03-09-2010)
hal-00495767 , version 5 (26-10-2010)
hal-00495767 , version 6 (04-11-2010)
hal-00495767 , version 7 (18-11-2010)
hal-00495767 , version 8 (20-10-2011)
hal-00495767 , version 9 (19-12-2011)

Identifiers

  • HAL Id : hal-00495767 , version 9

Cite

Bernard Candelpergher, Marc-Antoine Coppo. A new class of identities involving Cauchy numbers, harmonic numbers and zeta values. Ramanujan Journal (The), 2012, 27, pp.305-328. ⟨hal-00495767v9⟩
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