Representations of the Glaisher-Kinkelin constant deduced from integrals due to Féaux and Kummer

2024/10/11 by Jean‐Christophe Pain, Pain, Jean-Christophe
Mathematics · #FOS: Mathematics #Functional Equations Stability Results #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.2410.22338

openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. The calculations are based on definite integral expressions of logΓ(x), Γ being the usual Gamma function, due respectively to Féaux and Kummer. The connection between the second formula and an infinite series expansion of the Glaisher-Kinkelin constant is also outlined.

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