Peter Clarkson (University of Kent)

Wednesday 1st April, 2020 14:00-15:00 Zoom meeting ID: 864 150 864


In this talk I will discuss the relationship between orthogonal polynomials with respect to semiclassical weights, which are generalisations of the classical weights and arise in applications such as random matrices, and integrable systems, in particular the Painleve equations and discrete Painleve equations. Specifically I shall be concerned with generalised Freud weights, in particular the quartic and sextic weights. It is well-known that orthogonal polynomials satisfy a three-term recurrence relation. I will show that for quartic Freud weight the coefficients in the recurrence relation are expressed in terms of special function solutions of the fourth Painleve equation and for the sextic Freud weight in terms of solutions of Wronskians of generalised hypergeometric functions.

This is joint work with Kerstin Jordaan (University of South Africa).


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