Some supercongruences arising from symbolic summation

Liu, Ji-Cai

doi:10.1016/j.jmaa.2020.124062

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Cited by 9 publications

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“…The identities (2.1) and (2.2) are discovered and proved by the symbolic summation package Sigma developed by Schneider [18]. One can also refer to [12,13] for the same approach to finding and proving identities of this type.…”

Section: Preliminary Resultsmentioning

confidence: 99%

Supercongruences for sums involving Domb numbers

Liu

2020

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We prove some supercongruence and divisibility results on sums involving Domb numbers, which confirm four conjectures of Z.-W. Sun and Z.-H. Sun. For instance, by using a transformation formula due to Chan and Zudilin, we show that for any prime p ≥ 5,which is regarded as a p-adic analogue of the following interesting formula for 1/π due to Rogers:Here Domb(n) and E n are the famous Domb numbers and Euler numbers.

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Section: Preliminary Resultsmentioning

confidence: 99%