On Van Hamme's (A.2) and (H.2) supercongruences

In 1997, Van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)–(M.2). Using some combinatorial identities discovered by Sigma, we extend (A.2) and (H.2) to supercongruences modulo p4 for primes p≡3(mod4), which appear to be new.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-03, Vol.471 (1-2), p.613-622
Main Author: Liu, Ji-Cai
Format: Article
Language:English
Subjects:
Hypergeometric series
p-adic Gamma functions
Supercongruences
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Summary:In 1997, Van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)–(M.2). Using some combinatorial identities discovered by Sigma, we extend (A.2) and (H.2) to supercongruences modulo p4 for primes p≡3(mod4), which appear to be new.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.10.095