On Series Involving Cubed Catalan Numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917378348023808 |
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| author | Adegoke, Kunle |
| author_facet | Adegoke, Kunle |
| contents | Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a family of series containing fourth powers of Catalan numbers. Finally, we find a generalization of the Bauer series for $1/π$ and obtain some Ramanujan-like series for $1/π^2$ and~$1/π^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01249 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Series Involving Cubed Catalan Numbers Adegoke, Kunle Number Theory Combinatorics 05A10, 05A19 Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a family of series containing fourth powers of Catalan numbers. Finally, we find a generalization of the Bauer series for $1/π$ and obtain some Ramanujan-like series for $1/π^2$ and~$1/π^3$. |
| title | On Series Involving Cubed Catalan Numbers |
| topic | Number Theory Combinatorics 05A10, 05A19 |
| url | https://arxiv.org/abs/2604.01249 |