A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913961612410880 |
|---|---|
| author | Chen, Shaoshi Du, Hao Gao, Yiman Huang, Hui Li, Ziming |
| author_facet | Chen, Shaoshi Du, Hao Gao, Yiman Huang, Hui Li, Ziming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping Chen, Shaoshi Du, Hao Gao, Yiman Huang, Hui Li, Ziming Symbolic Computation 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. |
| title | A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping |
| topic | Symbolic Computation |
| url | https://arxiv.org/abs/2501.03837 |