Abstract
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey–Wilson polynomials. They are obtained from the original Wilson and Askey–Wilson polynomials by multiple applications of the discrete analogue of the Darboux transformations or the Crum–Krein–Adler deletion of ‘virtual state solutions’ of types I and II, in a similar way to the multi-indexed Laguerre, Jacobi and (q-)Racah polynomials reported earlier.
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