English

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

R2 v1 2026-06-21T23:47:03.556Z