Exceptional Bannai-Ito polynomials
Classical Analysis and ODEs
2018-12-20 v2
Abstract
We construct a non-trivial type of 1-step exceptional Bannai-Ito polynomials which satisfy discrete orthogonality by using a generalized Darboux transformation. In this generalization, the Darboux transformed Bannai-Ito operator is directly obtained through an intertwining relation. Moreover, the seed solution, which consists of a gauge factor and a polynomial part, plays an important role in the construction of these 1-step exceptional Bannai-Ito polynomials. And we show that there are 8 classes of gauge factors. We also provide the eigenfunctions of the corresponding multiple-step exceptional Bannai-Ito operator which can be expressed as a 3 x 3 determinant.
Cite
@article{arxiv.1711.08049,
title = {Exceptional Bannai-Ito polynomials},
author = {Yu Luo and Satoshi Tsujimoto},
journal= {arXiv preprint arXiv:1711.08049},
year = {2018}
}
Comments
30 pages