Two integral representations for the logarithm of the Glaisher-Kinkelin constant
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913345002536960 |
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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. Both are based on a definite integral of $\ln[Γ(x + 1)]$, $Γ$ being the usual Gamma function. The first one relies on an integral representation of $\ln[Γ(x + 1)]$ due to Binet, and the second one results from the so-called Malmstén formula. The numerical evaluation is easier with the latter expression than with the former. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two integral representations for the logarithm of the Glaisher-Kinkelin constant Pain, Jean-Christophe General Mathematics We present two integral representations of the logarithm of the Glaisher-Kinkelin constant. Both are based on a definite integral of $\ln[Γ(x + 1)]$, $Γ$ being the usual Gamma function. The first one relies on an integral representation of $\ln[Γ(x + 1)]$ due to Binet, and the second one results from the so-called Malmstén formula. The numerical evaluation is easier with the latter expression than with the former. |
| title | Two integral representations for the logarithm of the Glaisher-Kinkelin constant |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2405.05264 |