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Journal Articles Research in Number Theory Year : 2024

Generalized Glaisher-Kinkelin constants and Ramanujan summation of series

Abstract

We study a sequence of constants known as the Bendersky-Adamchik constants which appear quite naturally in number theory and generalize the classical Glaisher-Kinkelin constant. Our main initial purpose is to elucidate the close relation between the logarithm of these constants and the Ramanujan summation of certain divergent series. In addition, we also present a remarkable, and previously unknown, expansion of the logarithm of these constants in convergent series involving the Bernoulli numbers of the second kind.
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Dates and 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)
hal-03197403 , version 23 (03-06-2024)

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Marc-Antoine Coppo. Generalized Glaisher-Kinkelin constants and Ramanujan summation of series. Research in Number Theory, 2024, 10, pp.8. ⟨10.1007/s40993-023-00505-2⟩. ⟨hal-03197403v23⟩
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