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(2015.8.9 15:30 N702)Prof. Peter A Clarkson: Semi-classical orthogonal polynomials and the Painleve equations
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Update time: 2015-08-07
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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.
 

 

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