Special functions afternoon at KdV Institute

On Wednesday afternoon, April 16, 2008 there will be three lectures on special functions at the Korteweg-de Vries Institute of the University of Amsterdam. In the morning of the same day the lecture in the Algemeen Wiskunde Colloquium of the KdV Institute will also be on special functions: Frits Beukers (University of Utrecht) speaks at 11.15 hour on Algebraic hypergeometric functions, see the colloquium page.

The program of the afternoon is as follows:

14.00-14.45   Wolter Groenevelt (Institute of Applied Mathematics, Delft University of Technology),
A Hecke algebra approach to Wilson polynomials and Wilson functions

15.00-15.45   Natig Atakishiyev (IIMAS-Cuernavaca, Universidad Nacional Autónoma de México),
On integral and finite Fourier transforms of continuous q-Hermite polynomials of Rogers

16.00-16.45   Fokko van de Bult (KdV Institute, University of Amsterdam),
The symmetries of the 2φ1

Location:   Room P.015B, Euclides building, Plantage Muidergracht 24, Amsterdam

Date and time:   Wednesday April 16, 2008, 14.00-17.00 hour

Information:   Tom Koornwinder

Abstract Groenevelt
Cherednik's double affine Hecke algebras provide an algebraic structure that explains many fundamental properties of the Macdonald polynomials and Koornwinder polynomials. In this talk I explain how Wilson polynomials and Wilson functions (in one variable) fit into a similar algebraic framework.

Abstract Atakishiyev
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Abstract van de Bult
It is well-known that the 2φ1 satisfies the Heine transformation formulas. It is generally assumed these are the only transformations relating a 2φ1 with general parameters to another 2φ1. We will give a proof that Heine's transformations are indeed all possible transformations (and of course first define what we mean by this statement). An important idea in the proof is the philosophy that a function is almost completely determined by the q-difference equations it satisfies.

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