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

Satoru Odake

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.

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 -Jacobi and little -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 -Jacobi and little -Laguerre orthogonal polynomials.
Paper Structure (16 sections, 94 equations)

This paper contains 16 sections, 94 equations.

Table of Contents

  1. Introduction
  2. Darboux Transformations for rdQM
  3. rdQM systems
  4. Multi-step Darboux Transformations
  5. type $\text{I}$ construction for semi-infinite systems
  6. type $\text{II}$ construction for semi-infinite systems
  7. Multi-indexed Little $q$-Jacobi polynomials
  8. Original system
  9. Type $\text{I}$ polynomials
  10. Type $\text{II}$ polynomials
  11. Examples
  12. Multi-indexed Little $q$-Laguerre polynomials
  13. Original system
  14. Type $\text{I}$ polynomials
  15. Type $\text{II}$ polynomials
  16. ...and 1 more sections