MultiIntegrate

The MultiIntegrate package allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums.

Authors

Jakob Ablinger
The MultiIntegrate package 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 Carsten Schneider. It will be given for free to all researchers and non-commercial users. Copyright © 1999–2025 The RISC Computer Algebra and Applications 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.

The Package

The package is contained in the Mathematica input file and is accompanied by the Mathematica notebook:
  • demo.nb   (for Mathematica version 11.3)
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.

Literature

The theoretical background of the algorithms implemented in MultiIntegrate is described in
  • Computer Algebra Algorithms for Special Functions in Particle Physics (PhD Thesis). RISC, Johannes Kepler University, April 2012.[pdf]
  • J. Ablinger, A. Behring, J. Blümlein,A. De Freitas,A. von Manteuffel and C. Schneider. Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra.Comput. Phys. Comm. 202, pp. 33-112. 2016. ISSN 0010-4655. arXiv:1509.08324 [hep-ph].[url]
The PhD thesis also contains a chapter about how to use the package.

Bugs

Please report any bugs, comments and requests to Jakob Ablinger.