Type II Multi-indexed Little $q$-Jacobi and Little $q$-Laguerre Polynomials

Abstract

For the isospectral Darboux transformations of the discrete quantum mechanics with real shifts, there are two methods: type I and type II constructions. Based on the type I construction, the type I multi-indexed little $q$-Jacobi and little $q$-Laguerre orthogonal polynomials were presented in J. Phys. {\bf A50} (2017) 165204. Based on the type II construction, we present the type II multi-indexed little $q$-Jacobi and little $q$-Laguerre orthogonal polynomials.

25 pages. Comments and examples are added. To appear in JMP

References in corpus (5)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Orthogonal Polynomials from Hermitian Matrices
• Dual Christoffel transformations
• Multi-indexed Meixner and Little $q$-Jacobi (Laguerre) Polynomials
• Markov Chains Generated by Convolutions of Orthogonality Measures

Cited by in corpus (1)

• Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes