A curious $q$-analogue of Hermite polynomials
Combinatorics
2010-06-18 v4 Classical Analysis and ODEs
Abstract
Two well-known -Hermite polynomials are the continuous and discrete -Hermite polynomials. In this paper we consider a new family of -Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with -Fibonacci and -Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula.
Cite
@article{arxiv.0905.0228,
title = {A curious $q$-analogue of Hermite polynomials},
author = {Johann Cigler and Jiang zeng},
journal= {arXiv preprint arXiv:0905.0228},
year = {2010}
}
Comments
17 pages