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arXiv · 2101.06576

Telescopers for differential forms with one parameter

Shaoshi Chen·Ruyong Feng·Ziming Li·Michael F. Singer·Stephen Watt
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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.

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Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer, Stephen Watt. 2021-01-17. Telescopers for differential forms with one parameter. https://arxiv.org/abs/2101.06576

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