Representations of the Glaisher-Kinkelin constant deduced from integrals due to Féaux and Kummer
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917822173544448 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of the Glaisher-Kinkelin constant deduced from integrals due to Féaux and Kummer Pain, Jean-Christophe General Mathematics 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. |
| title | Representations of the Glaisher-Kinkelin constant deduced from integrals due to Féaux and Kummer |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2410.22338 |