On factorization of 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 (Dq2 - 1)Hn(x|q)=(q-n-1)Hn(x|q), where Dq is some explicitly known q-difference operator. This means that the polynomials Hn(x|q) are in fact governed by the q-difference equation DqHn(x|q)=q-n/2Hn(x|q), which is simpler than the conventional one.
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