Generalized Glaisher-Kinkelin constants, Blagouchine’s integrals, and Ramanujan summation of series
Résumé
The main motivation for this article is to establish a connection between a sequence of constants of Glaisher-Kinkelin type (known as the Bendersky- Adamchik constants) which appear quite naturally in number theory, and a family of complex integrals recently introduced by Blagouchine. Furthermore, we also elucidate the close relation between these constants and the Ramanujan summa- tion of certain divergent series, and we give a new convergent series expansion for the logarithm of these constants.
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