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The one-variable non-symmetric Wilson polynomials are shown to coincide withthe Bannai-Ito polynomials. The isomorphism between the correspondingdegenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and theBannai-Ito algebra is established. The Bannai-Ito polynomials are seen tosatisfy an orthogonality relation with respect to a positive-definite andcontinuous measure on the real line. A non-compact form of the Bannai-Itoalgebra is introduced and a four-parameter family of its infinite-dimensionaland self-adjoint representations is exhibited.

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