q-Rational reduction and q-analogues of series for π

Wang, Ronghua; Zhong, Michael X. X.

doi:10.1016/j.jsc.2022.08.020

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2024

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Cited by 3 publications

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“…This polynomial reduction was employed by Hou and Li [6] to derive new hypergeometric identities. A q-analogue of the Hou-Mu-Zeilberger reduction has also been introduced to prove and discover q-identities automatically [15]. Recently, the authors generalized the Hou-Mu-Zeilberger reduction to the holonomic case in [16].…”

Section: Introductionmentioning

confidence: 99%

Power-Partible Reduction and Congruences

Wang¹,

Zhong²

2023

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Based on the polynomial reduction, a holonomic (or, P-recursive) sequence F (k) can be decomposed into a summable part and a reduced part. In this paper, we show that when F (k) has a certain kind of symmetry, the reduced part contains only odd or even powers. The reduction in this case is called a power-partible reduction, which is then applied to obtain new series of congruences for Apéry numbers A k and central Delannoy polynomials D k (z). In particular, when p > 3 is a prime, we prove that for each r ∈ N, there is a p-adic integer c r such that p−1 k=0 (2k + 1) 2r+1 A k ≡ c r p (mod p 3 ).

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Section: Introductionmentioning

confidence: 99%