Abstract
Motivated by Zudilin’s work, we give q-analogues of the Ramanujan-type supercongruences (E.2) and (F.2) of Van Hamme. Our proof utilizes the q-WZ method and properties of cyclotomic polynomials. Using the same q-WZ pair, we also give q-analogues of some similar supercongruences due to He and Swisher. Additionally, we propose several related conjectures on supercongruences or q-supercongruences.
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This work was partially supported by the National Natural Science Foundation of China (Grant 11771175), the Natural Science Foundation of Jiangsu Province (Grant BK20161304), and the Qing Lan Project of Education Committee of Jiangsu Province.
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Guo, V.J.W. q-Analogues of the (E.2) and (F.2) supercongruences of Van Hamme. Ramanujan J 49, 531–544 (2019). https://doi.org/10.1007/s11139-018-0021-z
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DOI: https://doi.org/10.1007/s11139-018-0021-z