"Extensions of the AZ-algorithm and the Package MultiIntegrate"
, in J. Blümlein, C. Schneider: Anti-Differentiation and the Calculation of Feynman Amplitudes, Serie Texts & Monographs in Symbolic Computation (A Series of the Research Inst. of Symb. Comp., JKU,Linz), Springer, Seite(n) 35--61, 2021, ISBN: 978-3-030-80218-9
Extensions of the AZ-algorithm and the Package MultiIntegrate
Sprache des Titels:
Anti-Differentiation and the Calculation of Feynman Amplitudes
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. arXiv:2101.11385 [cs.SC]
Sprache der Kurzfassung:
Texts & Monographs in Symbolic Computation (A Series of the Research Inst. of Symb. Comp., JKU,Linz)