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A new extension of the (A.2) supercongruence of Van Hamme. (English) Zbl 1508.33015

Summary: We give a new extension of Van Hamme’s (A.2) supercongruence with a parameter \(s\) by establishing a \(q\)-analogue of this result. Our proof uses the ‘creative microscoping’ method, which was developed by the author and Zudilin. We also put forward some related open problems for further study.

MSC:

11A07 Congruences; primitive roots; residue systems
11B65 Binomial coefficients; factorials; \(q\)-identities
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
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