Two Finite Sequences of Symmetric q-Orthogonal Polynomials Generated by Two q-Sturm–Liouville Problems. Issue 1 (February 2020)

• Record Type: Journal Article
• Authors: Masjed-Jamei, Mohammad; Soleyman, Fatemeh; Koepf, Wolfram
• Is Part Of: Reports on mathematical physics. Volume 85:Issue 1(2020)
• Page Start: 41
• Page End: 55
• Publication Date: 2020-02
• Subjects: q-Sturm–Liouville problems -- symmetric finite q-orthogonal polynomials -- Ramanujan's identity -- little q-Jacobi polynomials -- norm square value; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(20)30009-4
• Languages: English
• ISSNs: 0034-4877

Abstract

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.