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arXiv · 2410.22338

Representations of the Glaisher-Kinkelin constant deduced from integrals due to F\'eaux and Kummer

Jean-Christophe Pain
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Abstract

We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. The calculations are based on definite integral expressions of $\log\Gamma(x)$, $\Gamma$ being the usual Gamma function, due respectively to F\'eaux 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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Jean-Christophe Pain. 2024-10-11. Representations of the Glaisher-Kinkelin constant deduced from integrals due to F\'eaux and Kummer. https://arxiv.org/abs/2410.22338

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