An integral representation of Catalan numbers using Malmstén's formula
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929537323892736 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | In this article, we propose an integral expression of the Catalan numbers, based on Malmstén's definite-integral representation of $\ln\left[Γ(x)\right]$, $Γ$ being the usual Gamma function. The obtained expression is likely to yield new summations involving Catalan numbers or central binomial coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An integral representation of Catalan numbers using Malmstén's formula Pain, Jean-Christophe Combinatorics Number Theory In this article, we propose an integral expression of the Catalan numbers, based on Malmstén's definite-integral representation of $\ln\left[Γ(x)\right]$, $Γ$ being the usual Gamma function. The obtained expression is likely to yield new summations involving Catalan numbers or central binomial coefficients. |
| title | An integral representation of Catalan numbers using Malmstén's formula |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2408.05130 |