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: Reduction formulas for multivariate hypergeometric series

Speaker: **Vladimir Retakh**, Rutgers University

Date: April 7, 2005 4:30-5:30pm

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

Abstract:

A hypergeometric series $F$ depends on of two sets: parameters $A=(a_1, a_2,..., a_N)$ and variables $X=(x_1, x_2,..., x_n)$.

A classical problem: For which sets of parameters the series $F$ can be written as a series $G$ with a lesser number of parameters $B=(b_1, b_2,..., b_M)$ and variables $Y=(y_1, y_2,..., y_m)$ where elements of $B$'s are rational expressions in $a_i$'s and elements of $Y$ are rational expressions in $y_j$'s. Such expressions are called reduction formulas.

A series of reduction formulas was constructed in 1993 by Gelfand, Graev and Retakh as a by-product of a sophisticated geometrical machine. An elementary proof of the simplest formula of Gelfand, Graev and Retakh was given recently by C. Krathenthaler. I would like to discuss a possibility of proving the reduction formulas by Zeilberger-Wilf method.