A characterization of some q-orthogonal polynomials

Abstract

We show that the only orthogonal polynomials satisfying a q-difference equation of the form π(x)D q P n (x) = (α n x + β n )P n (x) + γ n P n−1(x) where π(x) is a polynomial of degree 2, are the Al-Salam Carlitz 1, little and big q-Laguerre, the little and big q-Jacobi, and the q-Bessel polynomials. This is a q-analog of the work carried out in [1].