• Corpus ID: 10885090

Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals

@article{Ablinger2012AdvancedCA,
  title={Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals},
  author={Jakob Ablinger and Johannes Bl{\"u}mlein and Mark Round and Carsten Schneider},
  journal={ArXiv},
  year={2012},
  volume={abs/1210.1685}
}
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter $n$. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist--Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field… 

Extensions of the AZ-algorithm and the Package MultiIntegrate

  • J. Ablinger
  • Mathematics
    Texts & Monographs in Symbolic Computation
  • 2021
The Mathematica package MultiIntegrate, can be considered as an enhanced implementation of the (continuous) multivariate Almkvist Zeilberger algorithm to compute recurrences or differential equations for hyperexponential integrands and integrals.

Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms

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