The Paule/Schorn Implementation of Gosper's and Zeilberger's Algorithms
Short Description
With
Gosper's algorithm you can find closed forms for
indefinite hypergeometric sums. If you do not succeed, then you may
use
Zeilberger's algorithm to come up with a recurrence relation
for that sum. Both algorithms may be used to find and prove identities involving
hypergeometric terms and sums of those.
Registration and Legal Notices
The source code for this package is password protected. To get the password
send an email to
Peter Paule.
It will be given for free to all researchers and non-commercial users.
Copyright © 1999–2011 The RISC Combinatorics Group, Austria — all rights reserved.
Commercial use of the software is prohibited without prior written permission.
A Note on Encoded Files
This package contains one or more Mathematica input files which are encoded. Those files
cannot be read or modified directly as plain text, but can be loaded into
Mathematica just like any normal input file (i.e., with
<<"file" or
Get["file"]).
There is no need (and also no way) to decode them by using additional software
or a special key.
If loading an encoded file causes a syntax error, open it with a
text editor and remove any blank lines at the beginning (for some
reason your Mac could have inserted them silently...).
The Package
The
Paule/
Schorn
implementation of Gosper's and Zeilberger's algorithm
is contained in the Mathematica input file
and is accompanied by the Mathematica notebook
Screenshot
Click
here to see Gosper's
and Zeilberger's algorithms in action.
Literature
To use the implementation it is sufficient to study the notebook
readme.nb. It contains a few examples to start with.
You find some easy and several more involved examples for using the
implementation in our joint paper
P. Paule and M. Schorn,
A Mathematica Version of Zeilberger's Algorithm for Proving
Binomial Coefficient Identities,
J. Symbolic Comput., 20 (1995), 673-698.
[pdf]
The diploma thesis of Markus Schorn makes sure that the algorithm is indeed correct. Our
implementation is closely related to the detailed background developed there.
And again it contains several interesting examples.
M. Schorn,
Contributions to Symbolic Summation, Diploma Thesis, RISC,
J. Kepler University, Linz, December 1995.
[pdf]
Methods for tuning the algorithm are described in the paper
A. Riese,
Fine-Tuning Zeilberger's Algorithm: The Methods of Automatic Filtering and
Creative Substituting,
in Symbolic Computation, Number Theory, Special Functions, Physics
and Combinatorics (F.G. Garvan and M.E.H. Ismail, eds.),
Developments in Mathematics, Vol. 4, pp. 243-254, Kluwer, 2001.
[pdf]
Finally, in the book
A = B by M. Petkovsek, H. Wilf, and D. Zeilberger you find a collection
of methods to automatically prove identities.
Versions and Bugs
Right now you are using Version 3.52 last updated on January 12, 2005.
Please report any bugs and comments to
Peter Paule
or
Ralf Hemmecke.