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<p>We adapt the theory of normal and special polynomials from symbolic integration to the summation setting and then build up a general framework embracing both the usual shift case and the <i>q</i>-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 <i>q</i>-analogues. Our algorithms allow us to split up the usual shift case and the <i>q</i>-shift case only when it is really necessary, and thus instantly reveal the intrinsic differences between these two cases. Computational experiments are also provided.</p>

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A unified reduction for hypergeometric and q-hypergeometric creative telescoping

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Shaoshi Chen,
  • Hao Du,
  • Yiman Gao,
  • Hui Huang,
  • Ziming Li

摘要

We adapt the theory of normal and special polynomials from symbolic integration to the summation setting and then build 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 us 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.