A q-analogue of the (L.2) supercongruence of Van Hamme

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:466

Article

Guo, Victor J. W.¹ 

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

关键词: q-Binomial coefficients;    q-WZ method;    Cyclotomic polynomials;    q-Camma function;    Jackson's (6)phi(5) summation;   

DOI  :  10.1016/j.jmaa.2018.06.023

来源: Elsevier

【 摘 要 】

The (L.2) supercongruence of Van Hamme was proved by Swisher recently. In this paper we provide a conjectural q-analogue of the (L.2) supercongruence of Van Hamme and prove a weaker form of it by using the q-WZ method. In the same way, we prove a complete q-analogue of the following congruence Sigma(n)(k=0)(6k + 1)((2k)(k))(3) (-512)(n-k) (math) 0 (mod 4(2n + 1)((2n)(n))), which was conjectured by Z.-W. Sun and confirmed by B. He. We also provide a conjectural q-analogue of another congruence proved by Swisher. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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