Telescopers for differential forms with one parameter
Abstract
Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them have been extensively studied in the past thirty years. In this paper, we introduce the notion of telescopers for differential forms with $D$-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2021
- DOI:
- 10.48550/arXiv.2101.06576
- arXiv:
- arXiv:2101.06576
- Bibcode:
- 2021arXiv210106576C
- Keywords:
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- Computer Science - Symbolic Computation;
- 68W30
- E-Print:
- 26 pages