Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
Mathematical Physics
2015-06-15 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
Ordinary orthogonal polynomials are uniquely characterized by the three term recurrence relations up to an overall multiplicative constant. We show that the newly discovered M-indexed orthogonal polynomials satisfy 3+2M term recurrence relations with non-trivial initial data of the lowest M+1 members. These include the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. The M=0 case is the corresponding classical orthogonal polynomials.
Cite
@article{arxiv.1303.5820,
title = {Recurrence Relations of the Multi-Indexed Orthogonal Polynomials},
author = {Satoru Odake},
journal= {arXiv preprint arXiv:1303.5820},
year = {2015}
}
Comments
27 pages. Comments and a reference added, reference information updated. To appear in J.Math.Phys