English

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

General Mathematics 2025-09-29 v1

Abstract

We introduce a family of regularized functionals gn(x)g_n(x) that generalize the Euler--Mascheroni constant γ\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.

Keywords

Cite

@article{arxiv.2509.22289,
  title  = {Beyond the Euler--Mascheroni Constant: A Family of Functionals},
  author = {Ken Nagai},
  journal= {arXiv preprint arXiv:2509.22289},
  year   = {2025}
}

Comments

5 pages, no figures. Short note