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A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping

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arxiv 2501.03837 v2 pith:D3BPWYVA submitted 2025-01-07 cs.SC

classification cs.SC
keywords caseshiftalgorithmcreativeframeworkgeneralhypergeometricreduction
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions

    cs.SC 2025-06 conditional novelty 7.0 of 10

    Complete reductions can be built recursively in towers of Sigma*-extensions, yielding faster refined and parameterized telescoping algorithms for nested harmonic sums.

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