On the connection and linearization problem for discrete hypergeometric \(q\)-polynomials (Q5937228)

The authors study connection problems of the form NEWLINE\[NEWLINEQ_n(q;x)=\sum_{k=0}^nc_{n,k}P_k(q;x),NEWLINE\]NEWLINE where \(\{Q_n(q;x)\}\) en \(\{P_n(q;x)\}\) are two families of discrete \(q\)-hypergeometric orthogonal polynomials defined on the same non-uniform lattice. They obtain explicit expressions for the coefficients \(c_{n,k}\) in terms of the polynomial coefficients of the second order difference equations satisfied by the \(q\)-hypergeometric orthogonal polynomials involved. Finally the results are illustrated by some examples involving \(q\)-Charlier polynomials.