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arXiv · 2602.10558

On Touchard's Identity: Generalizations and Related Results

Kunle Adegoke
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Abstract

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.

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Kunle Adegoke. 2026-03-01. On Touchard's Identity: Generalizations and Related Results. https://arxiv.org/abs/2602.10558

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