Nested integrals and rationalizing transformations. (English) Zbl 1487.68257
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., 395-422 (2021).
In this paper, the author provides an overview of some important computer algebra methods for computations with nested integrals over integrands involving square roots. In particular, rewrite rules are analyzed for conversion to and from associated nested sums. In addition, the author compares the holonomic systems approach and the differential field approach. In order to simplify rational integrands, the author provides a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval \([0,1]\) bijectively to itself.
For the entire collection see [Zbl 1475.81004].
For the entire collection see [Zbl 1475.81004].
Reviewer: Sonia Pérez Díaz (Madrid)
MSC:
| 68W30 | Symbolic computation and algebraic computation |
| 12H05 | Differential algebra |
| 33F10 | Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) |
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 81T18 | Feynman diagrams |
Software:
HarmonicSumsReferences:
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