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arXiv · 1711.08049

Exceptional Bannai-Ito polynomials

Yu Luo·Satoshi Tsujimoto
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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.

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Yu Luo, Satoshi Tsujimoto. 2017-11-01. Exceptional Bannai-Ito polynomials. https://doi.org/10.1016/j.jat.2018.12.003

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