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# Colloquium: Dr. Howard S. Cohl

## September 20 @ 2:00 pm - 3:30 pm

Free# The Askey-Wilson Polynomials, their Symmetric Sub-Families and *q*-Inverse Properties

**Dr. Howard S. Cohl**

*National Institute of Standards and Technology*

*Mathematician*

“We give a more precise symmetric parametric description for various properties of the Askey-Wilson polynomials including hypergeometric and *q*-integral representations. We study the symmetric *q*-inverse sub-families of the Askey-Wilson polynomials. We also study the continuous *q*-inverse ultraspherical/*q*-inverse Rogers polynomials. We examine basic hypergeometric representation and transformation formulae, limit transitions, connection relations, and generating functions and corresponding *q*-integrals for these families. We have also focused on the* q*-inverse generating function for continuous *q*-inverse ultraspherical polynomials. This generating function has the intriguing property in that it is able to cross the natural boundary at *q*=1. Using this generating function, we compute a *q*-inverse analogue of the Ismail-Simeonov expansion for the continuous *q*-inverse ultraspherical polynomial generating function. This leads to a new terminating quadratic transformation for basic hypergeometric functions.”

Light refreshments will be served @ 1:30pm in EMS E424A.