Austin Sun, Department of Pure Mathematics, University of Waterloo
"From Snake Oil to Wilf-Zeilberger Pairs: A Tale of Hypergeometric Identities"
In this talk, I will present two methods that allows one to prove a large class of hypergeometric identities. The first is the so-called “snake oil method”: as its name suggests, one may apply it to evaluate most sums involving hypergeometric terms that one can think of. The second is the method of Wilf-Zeilberger pairs, introduced by Herbert S. Wilf and Doron Zeilberger in the early 1990s. I will give some motivations for this method, demonstrate that it is widely applicable, and use it to prove combinatorial identities that are otherwise difficult to evaluate by hand. If I have time, I will discuss the formal theory of Wilf-Zeilberger pairs, and present an algorithm for determining when such pairs exist.