Riemann–Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: The Matrix Discrete Painlevé IV

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 explicit general example presented to illustrate theoretical results work. The non-Abelian extensions family discrete Painlevé IV equations discussed.