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Session III.7 - Special Functions and Orthogonal Polynomials


Laguerre matrix orthogonal polynomials: A Riemann-Hilbert Approach

Assil Fradi

Universidade de Aveiro, Portugal   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider matrix orthogonal polynomials related to Laguerre type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann–Hilbert problem we can derive first and second order differential relations satisfied by matrix orthogonal polynomials and the associated second kind functions . Finally, non-Abelian extensions of a family of discrete Painlevé d-PIV equations are obtained for the three term recurrence relation coefficients.

Joint work with AMÍLCAR BRANQUINHO (Universidade de Coimbra, Portugal), ANA FOULQUIÉ-MORENO (Universidade de Aveiro, Portugal) and MANUEL MAÑAS (Universidad Complutense de Madrid, Spain).

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