On the generalized Glaisher-Kinkelin constants and Blagouchine’s integrals
Résumé
The main purpose of this article is to establish a close connection between a sequence of complex integrals introduced by Blagouchine and some important mathematical constants, namely the generalized Glaisher-Kinkelin constants (also known as the Bendersky constants) which occur quite naturally in analysis and number theory. At the end of this study, we also use a formula of Candelpergher to deduce an interesting expression of the alternating series ∑n≥2 (−1)^n ζ(n)/n^s for complex values of s.
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