Series representations for the logarithm of the Glaisher-Kinkelin constant

2023/04/15 by Jean‐Christophe Pain, Pain, Jean-Christophe
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2304.07629

openalex publication_date 2023/04/15 · openalex created_date 2023/04/20 · openalex updated_date 2026/07/28

Abstract

In this note, we propose two series expansions of the logarithm of the Glaisher-Kinkelin constant. The relations are obtained using expressions of derivatives of the Riemann zeta function, and one of them involves hypergeometric functions.

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