On Touchard's Identity: Generalizations and Related Results
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917301819801600 |
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| author | Adegoke, Kunle |
| author_facet | Adegoke, Kunle |
| contents | Starting with a known polynomial identity, we derive two generalizations of Touchard's identity concerning Catalan numbers; one obtained using the Beta function and the other via a connection with Stirling numbers of the second kind. We subsequently establish several new combinatorial identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Touchard's Identity: Generalizations and Related Results Adegoke, Kunle Combinatorics Number Theory 05A19, 05A10 Starting with a known polynomial identity, we derive two generalizations of Touchard's identity concerning Catalan numbers; one obtained using the Beta function and the other via a connection with Stirling numbers of the second kind. We subsequently establish several new combinatorial identities. |
| title | On Touchard's Identity: Generalizations and Related Results |
| topic | Combinatorics Number Theory 05A19, 05A10 |
| url | https://arxiv.org/abs/2602.10558 |