Miscellaneous series with Cauchy and harmonic numbers and their interpretation as Ramanujan summation - Université Côte d'Azur Access content directly
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 alternat- ing series with zeta (or harmonic zeta) values; we then give, for each of them, their interpretation in terms of Ramanujan summation with the hope that this unusual interpretation of still little-known formulas should be useful for further research on the topic.
Fichier principal
Vignette du fichier
MiscellaneousSeries_with_CauchyNumbersV6.pdf (309.56 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

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 6

Cite

Marc-Antoine Coppo. Miscellaneous series with Cauchy and harmonic numbers and their interpretation as Ramanujan summation. 2022. ⟨hal-03814355v6⟩
136 View
73 Download

Share

Gmail Facebook X LinkedIn More