An Isomonodromy Interpretation of the Hypergeometric Solution of the   Elliptic Painlev\'e Equation (and Generalizations)
  We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlev\'e equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonov's elliptic beta integral. 
Eric M. Rains