Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians. which are deformations of those for the Wilson and Askey-Wilson polynomials in terms of a degree l (l = 1, 2 ....) eigenpolynomial. These polynomials are exceptional in the sense that they start from degree l >= 1 and thus not constrained by any generalisation of Bochner's theorem.
PHYSICS LETTERS B. 682(1):130-136 (2009)
PHYSICS LETTERS B 682 (1), 130-136, 2009-11-23
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