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Preprints, Working Papers, ... Year : 2022

Miscellaneous series with Cauchy and harmonic numbers and their interpretation as Ramanujan summation

Abstract

We provide an overview of several series identities involving Cauchy numbers and harmonic numbers, all of which are closely linked to certain alternating series with zeta (or harmonic zeta) values; we then give, for each of them, their interpretation in terms of Ramanujan summation. We believe that this unusual interpretation of still little-known formulas should be useful for further research on the topic.
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Dates and versions

hal-03814355 , version 1 (13-10-2022)
hal-03814355 , version 2 (19-10-2022)
hal-03814355 , version 3 (24-10-2022)
hal-03814355 , version 4 (09-11-2022)
hal-03814355 , version 5 (28-11-2022)
hal-03814355 , version 6 (13-12-2022)
hal-03814355 , version 7 (06-01-2023)
hal-03814355 , version 8 (03-03-2023)
hal-03814355 , version 9 (20-07-2023)
hal-03814355 , version 10 (06-08-2023)

Identifiers

  • HAL Id : hal-03814355 , version 1

Cite

Marc-Antoine Coppo. Miscellaneous series with Cauchy and harmonic numbers and their interpretation as Ramanujan summation. 2022. ⟨hal-03814355v1⟩
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