**
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 `EKHAD`

and
`qEKHAD`

, obtainable by
anonymous ftp from

`math.temple.edu`

, directory ```
pub/zeilberg/programs
```

or via Doron's home page
http://www.math.temple.edu/~zeilberg

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 `zeilb`

and
`qzeilb`

(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

`ftp.fwi.uva.nl`

, directory

`pub/mathematics/reports/Analysis/koornwinder/zeilbalgo.dir`

or via Tom's home page
http://turing.fwi.uva.nl/~thk/. The accompanying paper

T.H. Koornwinder,

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

```
> ?sumtools
```

The accompanying paper is:

W. Koepf,

Algorithm for m-fold hypergeometric summation,
*J. Symb. Comput.*** 20 **(1995), 399-417.

Wolfram Koepf also wrote a book manuscript about these topics:

W. Koepf,

Algorithmic Summation and Special Function Identities with Maple,
*To appear*.

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:

- P. Paule & M. Schorn,

A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities,*J. Symb. Comput.***20**(1995), 673-698. -
P. Paule & A. Riese,

A Mathematica*q*-analogue of Zeilberger's algorithm based on an algebraically motivated approach to*q*-hypergeometric telescoping, to appear in

"Special Functions, q-Series and Related Topics".

The Fields Institute Communications Series.

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.
See WWW:

`http://www.can.nl/~demo/CAOP/CAOP.html`

You can also approach this via Rene's home page
```
http://star.cs.vu.nl/~rene/
```

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