The non-symmetric Wilson polynomials are the Bannai-Ito polynomials

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The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type (C₁, C₁) and the Bannai-Ito algebra is established. The Bannai-Ito polynomials are seen to satisfy an orthogonality relation with respect to a positive-definite and continuous measure on the real line. A non-compact form of the Bannai-Ito algebra is introduced and a four-parameter family of its infinite-dimensional and self-adjoint representations is exhibited.