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arXiv · 2501.03837

A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping

Shaoshi Chen·Hao Du·Yiman Gao·Hui Huang·Ziming Li
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Abstract

We adapt the theory of normal and special polynomials from symbolic integration to the summation setting, and then built up a general framework embracing both the usual shift case and the $q$-shift case. In the context of this general framework, we develop a unified reduction algorithm, and subsequently a creative telescoping algorithm, applicable to both hypergeometric terms and their $q$-analogues. Our algorithms allow to split up the usual shift case and the $q$-shift case only when it is really necessary, and thus instantly reveal the intrinsic differences between these two cases. Computational experiments are also provided.

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Shaoshi Chen, Hao Du, Yiman Gao, Hui Huang, Ziming Li. 2025-01-07. A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping. https://doi.org/10.1007/s11139-025-01164-w

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