The paper sets up a Riemann-Hilbert problem for matrix Laguerre biorthogonal polynomials from a matrix Pearson equation, derives first- and second-order differential systems, and connects them to eigenvalue problems and matrix discrete Painlevé IV equations.
Freud, On the coefficients in the recursion formulae of orthogonal polynomials , Proceedings of the Royal Irish Academy Section A 76 (1976) 1-6
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Riemann-Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: Eigenvalue Problems and the Matrix Discrete Painlev\'e IV
The paper sets up a Riemann-Hilbert problem for matrix Laguerre biorthogonal polynomials from a matrix Pearson equation, derives first- and second-order differential systems, and connects them to eigenvalue problems and matrix discrete Painlevé IV equations.