Two Finite Sequences of Symmetric q-Orthogonal Polynomials Generated by Two q-Sturm–Liouville Problems. Issue 1 (February 2020) - Masjed-Jamei, Mohammad; Soleyman, Fatemeh; Koepf, Wolfram
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.