Further q-analogues of the (G.2) Supercongruence of Van Hamme
Yudong Liu, Xiaoxia Wang
TL;DR
This paper introduces new q-analogues of Swisher's supercongruence of Van Hamme, extending the original supercongruence to a broader q-congruence framework with multiple parameters.
Contribution
The paper proposes two new q-analogues of Swisher's supercongruence and a generalized q-congruence with parameters, expanding the scope of supercongruence results.
Findings
Two q-analogues of Swisher's supercongruence are established.
A new parameterized q-congruence encompassing various q-analogues is presented.
The results extend supercongruence theory to the q-analogue setting.
Abstract
In 2015, Swisher generalized the (G.2) supercongruence of Van Hamme to the modulus p^4. In this paper, we first propose two q-analogues of Swisher's supercongruence and then a new q-congruence with parameters %which including several different q-analogues of Swisher's supercongruence is present.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Mathematical Theories and Applications · Benford’s Law and Fraud Detection