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MultiSum

Short Description

MultiSum 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 Kurt Wegschaider, 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 Peter Paule. 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 <<"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 MultiSum package consists of the files

Screenshot

Click here for an automatic proof of the Apery-Schmidt-Strehl identity.

Literature

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
K. Wegschaider, Computer Generated Proofs of Binomial Multi-Sum Identities, Diploma Thesis, RISC, J. Kepler University, Linz, May 1997. [ps]

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. [pdf] (The original article is available on LINK.)

Versions and Bugs

Right now you are using Version 2.02beta last updated on February 21, 2005. Please report any bugs to Ralf Hemmecke.