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arXiv · 2509.22289

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

Ken Nagai
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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.

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Ken Nagai. 2025-09-26. Beyond the Euler--Mascheroni Constant: A Family of Functionals. https://arxiv.org/abs/2509.22289

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