An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities

by Herb Wilf and Doron Zeilberger.

Appeared in Invent. Math. 108 (1992), 575-633.

This is a WZ classic.

.ps version

.pdf version of preprint

.pdf version of reprint

Added Jan. 3, 2011: While it is a masterpiece, it was not as carefully copy-edited as it should be. I just dug out Don Knuth's critique . [Since it was written more than 17 years ago, I took the liberty of making this "private" letter public.]

Added Nov. 8. , 2011: Shaoshi Chen, Christoph Koutschan, and Garth Payne have recently solved the 20-year conjecture made in this paper. As soon as their paper is posted, I will put a link to it. Meanwhile watch Shaoshi Chen's fascinating lecture: part 1, part 2.

Added July 18, 2015: The long-awaited paper Proof of the Wilf-Zeilberger Conjecture by Shaoshi Chen and Christoph Koutschan is now available!

Added Feb. 13, 2017: Bryan Ek pointed out that the factor in front of F(n,k) on the right of p. 624, line 12, q^(n-k) should be q^(n-k+1) and (q^k-q^k) should be (q^k - q^b)

Doron Zeilberger's List of Papers

Doron Zeilberger's Home Page