Paper

Title: On Zeilberger's algorithm and its q-analogue: a rigorous description

Author: Tom H. Koornwinder

Email: T.H.Koornwinder@uva.nl

Download: pdf

Pages: 22

Publication history:

• June 1992: Report AM-R9207, CWI, Amsterdam
• 1993: slightly shorter version appeared as: On Zeilberger's algorithm and its q-analogue, J. Comput. Appl. Math. 48 (1993), 91-111.
• Revisions of 1992 CWI report: March 1994, August 1996, July 1998, December 2000, January 2001

Abstract: Gosper's and Zeilberger's algorithms for summation of terminating hypergeometric series as well as the q-versions of these algorithms are described in a very rigorous way. The paper is a companion to Maple V procedures implementing these algorithms. It concludes with the help information for these procedures.

Maple procedures

Author: Tom H. Koornwinder

Email: T.H.Koornwinder@uva.nl

Download:

• zeilb, help_zeilb, zeilbtest.mws (for Zeilberger's algorithm)
• qzeilb, help_qzeilb, qzeilbtest.mws (for the q-version of Zeilberger's algorithm)

History:

• April 1992: first version
• 28 September 1993: slightly revised version
• 29 August 1996: minor bugs corrected; adapted to Maple V, Release 4
• 16 July 1998: adapted to Maple V, Release 5
• 11 December 2000: minor revisions; adapted to Maple 6
• 5 January 2000: minor change in zeilbtest.mws

Abstract: Maple V procedures for summation of terminating hypergeometric and q-hypergeometric series by Zeilberger's algorithm. These are highly rewritten versions of D. Zeilberger's Maple original procedures written around 1990.

Remark: More powerful implementations of Zeilberger's algorithm have been written by Koepf and by Zeilberger in Maple and by Paule in Mathematica. See links to their software.