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arXiv · 1912.11571

The rational Heun operator and Wilson biorthogonal functions

Satoshi Tsujimoto·Luc Vinet·Alexei Zhedanov
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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 ${_{10}}\Phi_9$ are found to be solutions of a generalized eigenvalue problem involving rational Heun operators of the special "classical" kind.

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Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov. 2019-12-25. The rational Heun operator and Wilson biorthogonal functions. https://arxiv.org/abs/1912.11571

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