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

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Résumé

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 et 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)

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  • HAL Id : hal-03814355 , version 5

Citer

Marc-Antoine Coppo. Miscellaneous series with Cauchy and harmonic numbers and their interpretation as Ramanujan summation. 2022. ⟨hal-03814355v5⟩
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