Topic #13 --------------- OP-SF NET --------------- September 12, 1996
Below follows an update about implementations of the Zeilberger algorithm and its q-analogue, and accompanying papers and books.
1. The most recent versions of Doron Zeilberger's own Maple implementations
(see OP-SF Net 1.1, Topic #14) are
qEKHAD, obtainable by
anonymous ftp from
or via Doron's home page
An accompanying book, in fact covering much more appeared this summer:
M. Petkovsek, H.S. Wilf & D. Zeilberger, A=B, A.K. Peters, 1996.
2. Tom Koornwinder's Maple implementations
(see OP-SF Net 1.1, Topic #14) dating back
from 1992 have just been slightly revised and adapted to Maple V, Release 4.
They are obtainable by anonymous ftp from
or via Tom's home page http://turing.fwi.uva.nl/~thk/. The accompanying paper
On Zeilberger's algorithm and its q-analogue,
J. Comput. Appl. Math. 48 (1993), 91-111
has been adapted accordingly. The slightly revised version, with title "On Zeilberger's algorithm and its q-analogue: a rigorous description" is also available from the ftp site just mentioned.
3. Wolfram Koepf implemented Zeilberger's algorithm and certain extensions in Maple V, Release 4. (See OP-SF Net 1.9, Topic #5 for an earlier implementation by him in 1994.) The present implementation is part of the official distribution of Maple V, Release 4. It can be made operational by the two commands
> with(sumtools): > readlib(`sum/simpcomb`):
possibly followed, to get help, by
The accompanying paper is:
Algorithm for m-fold hypergeometric summation,
J. Symb. Comput. 20 (1995), 399-417.
Wolfram Koepf also wrote a book manuscript about these topics:
Algorithmic Summation and Special Function Identities with Maple,
The new package "code", to be used for the generation of recurrence and differential equations for sums and integrals, written in connection with this book can be obtained from his home page http://www.zib.de/koepf/
4. Peter Paule and M. Schorn implemented Zeilberger's algorithm in Mathematica (see OP-SF Net 1.3, Topic #10), while Peter Paule and Axel Riese similarly implemented the q-Zeilberger algorithm. These implementations are available on email request to Peter Paule. The accompanying papers are:
5. Rene Swarttouw used Koepf's Maple implementations of the Zeilberger
algorithm for an interactive package on World Wide Web for calculating
formulas for orthogonal polynomials belonging to the Askey-scheme.
You can also approach this via Rene's home page