Multiple integral representations of the Catalan's constant
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911667265208320 |
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| author | Gómez-Déniz, Emilio Sarabia, José María |
| author_facet | Gómez-Déniz, Emilio Sarabia, José María |
| contents | In this paper, we present several novel integral representations of Catalan's constant. We begin by deriving an initial result expressed as a double integral. Subsequently, as a consequence of this result, we establish a general theorem that enables the representation of Catalan's constant in terms of a single integral. Finally, we provide a multiple integral representation of Catalan's constant in dimensions greater than or equal to two using the Lerch function. The results are accompanied by illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiple integral representations of the Catalan's constant Gómez-Déniz, Emilio Sarabia, José María Number Theory aaA99, 11M35, 11Z99 In this paper, we present several novel integral representations of Catalan's constant. We begin by deriving an initial result expressed as a double integral. Subsequently, as a consequence of this result, we establish a general theorem that enables the representation of Catalan's constant in terms of a single integral. Finally, we provide a multiple integral representation of Catalan's constant in dimensions greater than or equal to two using the Lerch function. The results are accompanied by illustrative examples. |
| title | Multiple integral representations of the Catalan's constant |
| topic | Number Theory aaA99, 11M35, 11Z99 |
| url | https://arxiv.org/abs/2605.08899 |