A curious q-analogue of Hermite polynomials

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.

• Type: Journal
• Year: 2011
• Where: JCT
• Authors: Johann Cigler, Jiang Zeng
• Keywords: Discrete Q-Hermite Polynomials, JCT 2011, Q-Hermite Polynomials, Well-known Q-Hermite Polynomials