Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Peter A Clarkson,School of Mathematics, Statistics & Actuarial Science, University of Kent, UK
Inviter:
Title:
Semi-classical orthogonal polynomials and the Painleve equations
Time & Venue:
2015.8.9 15:30-16:30 N702
Abstract:
In this talk I shall discuss the relationship between the Painleve equations and orthogonal polynomials with respect to semi-classical weights. It is well-known that orthogonal polynomials satisfy a three-term recurrence relation. I will show that for some semi-classical weights, the coefficients in the recurrence relation can be expressed in terms of Wronskians that arise in the description of special function solutions of a Painleve equation. The orthogonal polynomials discussed will include semi-classical Laguerre and Hermite weights, a generalization of the Freud weight and semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials.
Appendix：
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