Two Finite Sequences of Symmetric q-Orthogonal Polynomials Generated by Two q-Sturm–Liouville Problems

Abstract

By using a symmetric generalization of Sturm–Liouville problems in q-difference spaces, we introduce two finite sequences of symmetric q-orthogonal polynomials and obtain their basic properties such as a second-order q-difference equations, the explicit form of the polynomials in terms of basic hypergeometric series, three-term recurrence relations and norm-square values based on a Ramanujan identity. We also show that one of the introduced sequences is connected with the little q-Jacobi polynomials.