Moments of Askey-Wilson polynomials

Combinatorics/Partitions Seminar

Meeting Details

For more information about this meeting, contact Matthew Katz, James Sellers, George Andrews.

Speaker: Jang Soo Kim, University of Minnesota

Abstract: The Askey-Wilson polynomials are the most general orthogonal polynomials among those classified by the Askey scheme. These are orthogonal polynomials in one variable with 5 parameters. In this talk I will talk about 3 combinatorial methods to study the nth moment of the Askey-Wilson polynomials. The first method is Viennot's theory of weighted Motzkin paths. The second method uses staircase tableaux introduced by Corteel and Williams. The third method is a modification of an idea of Ismail, Stanton, and Viennot on matchings and q-Hermite polynomials. Using the third method we express the nth moment as a fraction of two generating functions for certain matchings and obtain a new formula for the moment. This is joint work with Dennis Stanton.

Room Reservation Information

Room Number: 106 McAllister

Date: 04/09/2013

Time: 11:15am - 12:05pm