The non-symmetric Wilson polynomials are the Bannai-Ito polynomials (Q2827371)

In this paper, the authors identify the one-variable non-symmetric Wilson polynomials with the Bannai-Ito polynomials, and identify the corresponding degenerate double affine Hecke algebra of type \((C_1^\vee ;C_1)\) with the Bannai-Ito algebra by constructing an isomorphism. They also present a positive-definite and continuous measure on the real line for the Bannai-Ito polynomials, a non-compact form of the Bannai-Ito algebra, as well as a four-parameter family of its infinite-dimensional and self-adjoint representations.