Abstract
Abstract
We investigate a Riemann–Hilbert problem (RHP), whose solution corresponds to a group of q-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the polynomials approach infinity. The RHP formulation also enables us to obtain further properties. In particular, we consider how the class of polynomials and their asymptotic behaviours change under translations of the q-discrete lattice and determine the asymptotics of a related q-Painlevé equation.
Funder
Australian Government Research Training Program
Australian Research Council Discovery Projects
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
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