@incollection{RISC6408,author = {J. Ablinger},
title = {{Extensions of the AZ-algorithm and the Package MultiIntegrate}},
booktitle = {{Anti-Differentiation and the Calculation of Feynman Amplitudes}},
language = {english},
abstract = {We extend the (continuous) multivariate Almkvist-Zeilberger algorithm in
order to apply it for instance to special Feynman integrals emerging in renormalizable Quantum field Theories. We will consider multidimensional integrals over
hyperexponential integrals and try to find closed form representations in terms of
nested sums and products or iterated integrals. In addition, if we fail to compute
a closed form solution in full generality, we may succeed in computing the first
coeffcients of the Laurent series expansions of such integrals in terms of indefnite
nested sums and products or iterated integrals. In this article we present the corresponding methods and algorithms. Our 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. Together with the summation package
Sigma and the package HarmonicSums our package provides methods to compute
closed form representations (or coeffcients of the Laurent series expansions) of multidimensional integrals over hyperexponential integrands in terms of nested sums or
iterated integrals.},
series = {Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria)},
pages = {35--61},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-80218-9},
year = {2021},
note = {arXiv:2101.11385 [cs.SC]},
editor = {J. Blümlein and C. Schneider},
refereed = {yes},
keywords = {multivariate Almkvist-Zeilberger algorithm, hyperexponential integrals, iterated integrals, nested sums},
length = {27},
url = {https://doi.org/10.1007/978-3-030-80219-6_2}
}