Mixed recurrence relations and interlacing of the zeros of some q-orthogonal polynomials from different sequences

Abstract

We use the generating functions of some q-orthogonal polynomials to obtain mixed recurrence relations involving polynomials with shifted parameter values. These relations are used to prove interlacing results for the zeros of Al- Salam–Chihara, continuous q-ultraspherical, q-Meixner–Pollaczek and q-Laguerre polynomials of the same or adjacent degree as one of the parameters is shifted by integer values or continuously within a certain range. Numerical examples are given to illustrate situations where the zeros do not interlace.