Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: The Sharpening of WZ Theory

Speaker: **Mohamud Mohammed**, Rutgers University

Date: October 14, 2004 4:30-5:30pm

Location: Hill Center, Room 425, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

A new proof of the Fundamental Theorem for Hypergeometric (and q-Hypergeometric) summation/integration, that does not depend on Sister Celine's method will be presented. As a consequence, we get simplified versions of the Zeilberger, q-Zeilberger, and Almkvist-Zeilberger algorithms. We also considerably improve the upper bounds given, in 1992, by Wilf and Zeilberger, for the orders of the recurrences and differential equations outputted by these algorithms, and prove sharp. More importantly, using the new approach, we extend the above algorithms from one to several dimensions.

Joint work with Doron Zeilberger.