Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations

Abstract

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 $p_n$: $q_n=p_n+{\beta }_n{p}_{n-1}$, $β_n\in \RR$. 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.

18 pages. arXiv admin note: text overlap with arXiv:1302.0881, arXiv:1307.1326

References in corpus (1)

• Askey-Wilson Type Functions, With Bound States