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Two sets of infinitely many exceptional orthogonal polynomials related to theWilson and Askey-Wilson polynomials are presented. They are derived as theeigenfunctions of shape invariant and thus exactly solvable quantum mechanicalHamiltonians, which are deformations of those for the Wilson and Askey-Wilsonpolynomials in terms of a degree \ell (\ell=1,2,...) eigenpolynomial. Thesepolynomials are exceptional in the sense that they start from degree \ell\ge1and thus not constrained by any generalisation of Bochner's theorem.

physics letters b

Infinitely many shape invariant discrete quantum mechanical systems and  new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson  polynomials