is a Mathematica package for proving hypergeometric
multi-sum identities. It uses an efficient generalization of Sister
Celine's technique to find a homogeneous polynomial recurrence relation
for the sum. The package has been developed by
, a former member of the
RISC Combinatorics group
Registration and Legal Notices
The source code for this package is password protected. To get the password
send an email to
It will be given for free to all researchers and non-commercial users.
Copyright © 1999–2012 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
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...).
package consists of the files
for an automatic proof
of the Apery-Schmidt-Strehl identity.
A detailed description of the package and of the method
(a generalization of Sister Celine's technique) together with several examples
is contained in the diploma thesis
Computer Generated Proofs of Binomial Multi-Sum Identities, Diploma Thesis, RISC,
J. Kepler University, Linz, May 1997.
A more recent version of the implementation with its latest enhancements is described
by means of an example in the paper
R. Lyons, P. Paule, and A. Riese,
A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers,
Appl. Algebra Engrg. Comm. Comput., 13 (2002), 327-333.
(The original article is available on
Versions and Bugs
Right now you are using Version 2.02beta last updated on February 21, 2005. Please report any bugs