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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