On an extension of a Van Hamme supercongruence. (English) Zbl 1401.11053
Summary: We prove a conjectural extension of a van Hamme supercongruence [L. Van Hamme, Lect. Notes Pure Appl. Math. 192, 223–236 (1997; Zbl 0895.11051)] due to Z.-W. Sun [Ill. J. Math. 56, No. 3, 967–979 (2012; Zbl 1292.11040)]. The proof is inspired by recent techniques due to R. Osburn and W. Zudilin [J. Math. Anal. Appl. 433, No. 1, 706–711 (2016; Zbl 1400.11062)], in particular the use of a certain WZ pair and congruences for quotients of Pochhammer symbols.
MSC:
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 11A07 | Congruences; primitive roots; residue systems |
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