Beyond the Euler--Mascheroni Constant: A Family of Functionals

Abstract

We introduce a family of regularized functionals $g_n(x)$ that generalize the Euler--Mascheroni constant $\gamma$. They arise from a weighted regularization of Clausen-type trigonometric sums, and admit explicit integral representations, differential and ladder relations, together with an umbral generating function.

arXiv comment5 pages, no figures. Short note