%0 Journal Article
%T Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations
%A Renato ¨˘lvarez-Nodarse
%A Antonio J. Dur¨˘n
%J Mathematics
%D 2013
%I arXiv
%X Let $(p_n)_n$ be either the $q$-Meixner or the $q$-Laguerre polynomials. We form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of two consecutive $p_n$: $q_n=p_n+\beta_np_{n-1}$, $\beta_n\in \RR$. Using the concept of $\D$-operator, we generate sequences $(\beta_n)_n$ for which the polynomials $(q_n)_n$ are orthogonal with respect to a measure and common eigenfunctions of a higher order $q$-difference operator.
%U http://arxiv.org/abs/1309.3296v1