### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Proof of the Wilf-Zeilberger conjecture

Speaker: ** Shaoshi Chen**, North Carolina State University

Date: Thursday, October 20, 2011 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The method of creative telescoping was first formulated by Zeilberger in the early 1990's. Zeilberger's method has become a powerful tool in the study of special function identities. Algorithms for creative telescoping terminate on holonomic functions. However, the holonomicity of functions is difficult to detect algorithmically in general. In 1992, Wilf and Zeilberger conjectured that a hypergeometric function is holonomic if and only if it is proper. In this talk, I will present a proof of this conjecture with the help of an extension of the Ore-Sato theorem. According to some recent results, the properness of a hypergeometric function can be decided algorithmically via certain multiplicative decomposition of its certificates. So we get a bridge between the holonomicity and the properness of hypergeometric functions by turning the Wilf-Zeilberger conjecture into a theorem.
(This is a joint work with Christoph Koutschan and Garth Payne)

See: http://www.math.rutgers.edu/~bnaka/expmath/