The factorization of a q-difference equation for continuous q-Hermite polynomials

Abstract

We argue that a customary q-difference equation for the continuous q-Hermite polynomials Hn(x|q) can be written in the factorized form as , where is some explicitly known q-difference operator. This means that the polynomials Hn(x|q) are in fact governed by the q-difference equation , which is simpler than the conventional one. It is shown that a similar factorization holds for the continuous q−1-Hermite polynomials hn(x|q).