A two-variable extension of Bannai-Ito polynomials is presented. They are obtained via q → −1 limits of the bivariate q-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These new polynomials are also shown to be multispectral. Two Dunkl shift operators are seen to be diagonalized by the bivariate Bannai-Ito polynomials and 3- and 9-term recurrence relations are provided.
It might be possible to absorb this singularity with some fine-tuning of the parameters as has been done for the Racah and q-Racah polynomials,24,25 but this has not been explored yet and goes beyond the scope of this paper.