On Touchard's Identity: Generalizations and Related Results
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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Mathematical functions and polynomials
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint