A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping
Symbolic Computation
2025-07-29 v2
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 -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 -analogues. Our algorithms allow to split up the usual shift case and the -shift case only when it is really necessary, and thus instantly reveal the intrinsic differences between these two cases. Computational experiments are also provided.
Cite
@article{arxiv.2501.03837,
title = {A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping},
author = {Shaoshi Chen and Hao Du and Yiman Gao and Hui Huang and Ziming Li},
journal= {arXiv preprint arXiv:2501.03837},
year = {2025}
}