CLOSED FORM (pun intended!)

by Doron Zeilberger

Appeard in Contemporary Mathematics 143 (1993) (special volume in memory of Emil Grosswald, edited by Marvin Knopp and Mark Sheingorn),579-608.

It was Herb Wilf's brilliant insight that turned a mere algorithm (the so-called Zeilberger algorithm, a.k.a. as the Gosper-Zeilberger algorithm) into a full-fledged theory (WZ theory). This article is just a modest beginning to realizing its full potential. Even though, it has already found quite a few applications to series acceleration and it was exactly what was needed to conclude the Ahlgren- Ono proof of Beukers's conjecture.

(Plain ) .tex version (28 pages)

.dvi version (for previewing)

.ps version

.pdf version

The present Plain TeX version was obtained by applying my TroffToTeX translator to the original Troff source file

Note Added April 9, 2001: My brilliant and dedicated grad student, Mohamud Mohammed, found some slight misstatements in section 7, and the 1-forms are incorrect as stated. Please read Mohamud Mohammed's corrections in either latex (3 pages), .ps , or .pdf.

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