A curious $q$-analogue of Hermite polynomials

Details A curious $q$-analogue of Hermite polynomials A curious $q$-analogue of Hermite polynomials

2009-05-02

arxiv.org/abs/0905.0228v4

Mathematics

Combinatorics

17 pages

Scientific paper

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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