Second order q-difference equations solvable by factorization method

By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal polynomials, are discussed. It is shown that in the limit q->1 the present method corresponds to the one developed by Infeld and Hull.