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arXiv · 0905.0228

A curious $q$-analogue of Hermite polynomials

Johann Cigler·Jiang zeng
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Abstract

Two well-known $q$-Hermite polynomials are the continuous and discrete $q$-Hermite polynomials. In this paper we consider a new family of $q$-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with $q$-Fibonacci and $q$-Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula.

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Johann Cigler, Jiang zeng. 2010-06-17. A curious $q$-analogue of Hermite polynomials. https://arxiv.org/abs/0905.0228

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