English

Para-Bannai-Ito Polynomials

Classical Analysis and ODEs 2023-11-15 v3

Abstract

New bispectral polynomials orthogonal on a Bannai-Ito bi-lattice (uniform quadri-lattice) are obtained from an unconventional truncation of the untruncated Bannai-Ito and complementary Bannai-Ito polynomials. A complete characterization of the resulting para-Bannai-Ito polynomials is provided, including a three term recurrence relation, a Dunkl-difference equation, an explicit expression in terms of hypergeometric series and an orthogonality relation. They are also derived as a q1q\to -1 limit of the qq-para-Racah polynomials. A connection to the dual 1-1 Hahn polynomials is also established.

Keywords

Cite

@article{arxiv.2209.10725,
  title  = {Para-Bannai-Ito Polynomials},
  author = {Jonathan Pelletier and Luc Vinet and Alexei Zhedanov},
  journal= {arXiv preprint arXiv:2209.10725},
  year   = {2023}
}
R2 v1 2026-06-28T01:51:51.671Z