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Pré-Publication, Document De Travail Année : 2023

Generalized Glaisher-Kinkelin constants, Blagouchine’s integrals, and Ramanujan summation

Résumé

The main motivation of this article is to establish a connection between the generalized Glaisher-Kinkelin constants (also known as the Bendersky- Adamchik constants) which appear quite naturally in number theory, and a family of complex integrals introduced by Blagouchine. Furthermore, we also elucidate the close relation between these constants and the Ramanujan summation of certain divergent series, and finally we give a new convergent series expansion of the logarithm of these constants.
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Dates et versions

hal-03197403 , version 1 (13-04-2021)
hal-03197403 , version 2 (17-04-2021)
hal-03197403 , version 3 (04-05-2021)
hal-03197403 , version 4 (08-05-2021)
hal-03197403 , version 5 (10-05-2021)
hal-03197403 , version 6 (03-06-2021)
hal-03197403 , version 7 (10-06-2021)
hal-03197403 , version 8 (03-08-2021)
hal-03197403 , version 9 (04-08-2021)
hal-03197403 , version 10 (09-08-2021)
hal-03197403 , version 11 (25-08-2021)
hal-03197403 , version 12 (26-09-2021)
hal-03197403 , version 13 (01-10-2021)
hal-03197403 , version 14 (06-10-2021)
hal-03197403 , version 15 (13-10-2021)
hal-03197403 , version 16 (01-03-2022)
hal-03197403 , version 17 (02-03-2022)
hal-03197403 , version 18 (09-03-2022)
hal-03197403 , version 19 (19-12-2022)
hal-03197403 , version 20 (31-12-2022)
hal-03197403 , version 21 (08-03-2023)
hal-03197403 , version 22 (18-10-2023)

Identifiants

  • HAL Id : hal-03197403 , version 20

Citer

Marc-Antoine Coppo. Generalized Glaisher-Kinkelin constants, Blagouchine’s integrals, and Ramanujan summation. 2023. ⟨hal-03197403v20⟩
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