In this paper we solve an arbitrary matrix Riemann-Hilbert (inverse monodromy) problem with quasi-permutation monodromy representations outside of a divisor in the space of monodromy data. This divisor is characterized in terms of the theta-divisor on the Jacobi manifold of an auxiliary compact Riemann surface realized as an appropriate branched covering of CP 1 . The solution is given in terms...

In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve complex plane finite endpoint at origin, is used for study of corresponding matrix biorthogonal polynomials associated Laguerre type matrices weights—which are constructed in terms given Pearson equation. First and second order differential systems fundamental matrix, solution mentioned derived. An explici...

Abstract We investigate a Riemann–Hilbert problem (RHP), whose solution corresponds to group of q -orthogonal polynomials studied earlier by Ismail et al . Using RHP theory we determine new asymptotic results in the limit as degree approach infinity. The formulation also enables us obtain further properties. In particular, consider how class and their behaviours change under translations -discr...