The rational Heun operator and Wilson biorthogonal functions
Abstract
We consider the rational Heun operator defined as the most general second-order q-difference operator which sends any rational function of type [(n-1)/n] to a rational function of type [n/(n+1)]. We shall take the poles to be located on the Askey-Wilson grid. It is shown that this operator is related to the one-dimensional degeneration of the Ruijsenaars-van Diejen Hamiltonians. The Wilson biorthogonal functions of type 109 are found to be solutions of a generalized eigenvalue problem involving rational Heun operators of the special "classical" kind.
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