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Journal Articles Integers : Electronic Journal of Combinatorial Number Theory Year : 2023

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

Abstract

We provide an overview of several series identities involving the Cauchy numbers and various types of harmonic numbers, all of which are closely connected to certain alternating series with zeta values (or harmonic zeta values). We then give, for each of these identities, an interpretation in terms of Ramanujan summation with the hope that this unusual but interesting interpretation of still little-known formulas could inspire 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 10

Cite

Marc-Antoine Coppo. Miscellaneous series identities with Cauchy and harmonic numbers, and their interpretation as Ramanujan summation. Integers : Electronic Journal of Combinatorial Number Theory, 2023, 23, pp.10. ⟨hal-03814355v10⟩
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