Short Description

The MultiIntegrate package by Jakob Ablinger allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums. This package uses variations and extensions of the multivariate Alkmkvist-Zeilberger algorithm.

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 package is contained in the Mathematica input file and is accompanied by the Mathematica notebook: Right now you are using Version 1.0 released on October 11, 2018. This version is compatible with Mathematica versions from 9.0 to 11.3. Please report any bugs and comments Jakob Ablinger.


The theoretical background of the algorithms implemented in MultiIntegrate is described in The PhD thesis also contains a chapter about how to use the package.