Extensions of the AZ-algorithm and the package multiintegrate. (English) Zbl 07458361

Bluemlein, Johannes (ed.) et al., Anti-differentiation and the calculation of Feynman amplitudes. Selected papers based on the presentations at the conference, Zeuthen, Germany, October 2020. Cham: Springer. Texts Monogr. Symb. Comput., 35-61 (2021).
This paper presents an extension of the multivariate Almkvist-Zeilberger algorithm which can compute linear differential equations for multiple integrals with one parameter. The motivation of this extension is applying the method to solve some computational problems on Feynman integrals in Quantum Field Theory. A Mathematica package MultiIntegrate was developed by the author and some concrete examples are used to show the capability of this package. With this package, the author can first try to find closed form representations of multiple hyperexponential integrals in terms of nested sums and products or iterated integrals. If a closed form is not found, the author can still succeed in computing the first coefficients of the Laurent series expansions of such integrals. In order to speed-up the computation, the author also introduced a divide-and-conquer strategy in the algorithm. The methods, algorithms, and implementations in this paper enhance the applicability of the Almkvist-Zeilberger algorithm in real applications.
For the entire collection see [Zbl 1475.81004].


33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
Full Text: DOI arXiv


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