Multiple Askey-Wilson polynomials and other related multiple orthogonal polynomials

by Walter Van Assche (KU Leuven)

Location: 200B.02.18, Leuven
Time: Wednesday April 3, 2019 at 10:30

The Askey-Wilson polynomials are the most general family of basic hypergeometric polynomials and appear on top of the Askey table of classical orthogonal polynomials. We first show how Askey-Wilson polynomials can be obtained from little q-Jacobi polynomials by using a special linear transformation. Then we use this transformation to map multiple little q-Jacobi polynomials to multiple Askey-Wilson polynomials. These multiple little q-Jacobi polynomials were investigated earlier by Postelmans and Van Assche because they appear in irrationality proofs for a q-version of the zeta-function. In a similar way we find a linear transformation that maps multiple little q-Laguerre polynomials to multiple Al-Salam—Chihara polynomials and another transformation to continuous dual q-Hahn polynomials. This is joint work with Jean Paul Nuwacu from Université du Burundi.