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

Abstract

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 $p^4$ for primes $p\equiv 3(\mathrm{mod}4)$, which appear to be new.

9 pages

References in corpus (1)

• On the (K.2) supercongruence of Van Hamme