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 limit of the -para-Racah polynomials. A connection to the dual Hahn polynomials is also established.
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}
}