## 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 *_{2}φ_{1}

*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 _{2}φ_{1}
satisfies the Heine
transformation formulas. It is generally assumed these are the only
transformations relating a _{2}φ_{1}
with general parameters to
another _{2}φ_{1}.
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.

to Tom Koornwinder's home page