On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R1

Abstract

We study a polynomial sequence of q-extensions of the classical Hermite polynomials Hn(x), which satisfi es continuous orthogonality on the whole real line R with respect to the positive weight function. This sequence can be expressed either in terms of the q-Laguerre polynomials L n (x; q), = 1=2, or through the discrete q-Hermite polynomials ~hn(x; q) of type II.