Algebras behind the bispectrality of the Wilson rational functions and their ${}_4\phi_3$ limits
Mathematical Physics
2025-11-17 v2 math.MP
Abstract
The properties of the Wilson rational functions with three different normalizations are described. For one normalization, it satisfies an recurrence relation, whereas for the two other ones, they satisfy a generalized eigenvalue problem. The so-called Wilson rational algebra is introduced, which encodes algebraically the spectral properties of these special functions. Finally, different limits are considered, leading up to functions proportional to . For one of these, the spectral algebra simplifies to yield the meta -Racah algebra.
Keywords
Cite
@article{arxiv.2502.04275,
title = {Algebras behind the bispectrality of the Wilson rational functions and their ${}_4\phi_3$ limits},
author = {Nicolas Crampe and Satoshi Tsujimoto and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:2502.04275},
year = {2025}
}