# Special Lecture on q-Counting

The department is very pleased to announce the forthcoming lecture by Richard Askey. It will have a strong mathematics as well as mathematics education focus. I encourage all of you to attend. The talk will be aimed at undergraduates.

Thursday, November 15.

Refreshments at 4:00 followed by the talk at 4:30, in

Cuneo Hall, Room 311

**Speaker:** Richard Askey (University of Wisconsin)

Member of the U.S. National Academy of Sciences, and

Honorary Foreign Member of the Indian Academy of Sciences

**Title:** The binomial theorem, beta and gamma functions, and some extensions of each

**Abstract:** It is well known that the number of permutations of the set 1,2,..., *n* is *n*!. An extension of this where one counts inversions was posed as a problem by M. Stern in 1839. These will be the starting place to build up the binomial theorem, the extension of n! which we now write as the gamma function, the beta integral of John Wallis, Euler's integral representation of the gamma function, and the connection between these three things. This connection will be looked at in two different settings, the classical one which many of you know, and what will be called *q*-extensions of these classical results into a world which has finally started to come into its own.