Abstract
We construct a nontrivial type of 1-step exceptional Bannai–Ito polynomials which satisfy a 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 × 3 determinant.
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