On Touchard's Identity: Generalizations and Related Results
Combinatorics
2026-03-03 v3 Number Theory
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.
Keywords
Cite
@article{arxiv.2602.10558,
title = {On Touchard's Identity: Generalizations and Related Results},
author = {Kunle Adegoke},
journal= {arXiv preprint arXiv:2602.10558},
year = {2026}
}
Comments
15 pages, no figures or tables