arXiv: Number Theory | 2019
Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences
Abstract
We prove a kind of bilateral semi-terminating series related to Ramanujan-like series for negative powers of $\\pi$, and conjecture a type of supercongruences associated to them. We support this conjecture by checking all the cases for many primes. In addition we are able to prove a few of them from some terminating hypergeometric identities. Finally, we make an intriguing observation.