Equivalences of the Multi-Indexed Orthogonal Polynomials
arXiv:1309.2346 · doi:10.1063/1.4859795
Abstract
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.
25 pages. Some comments and a reference added. To appear in J.Math.Phys
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- Shape invariance and equivalence relations for pseudowronskians of Laguerre and Jacobi polynomials
- Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
- Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
- Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
- New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
- Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types
- Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts