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 ${}_{10}{\Phi }_9$ are found to be solutions of a generalized eigenvalue problem involving rational Heun operators of the special "classical" kind.

14 pages, 21 references

Cited by in corpus (1)

• An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type