Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences

Jesús Guillera

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arXiv · 1908.05123

Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences

Jesús Guillera

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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.

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Jesús Guillera. 2019-08-14. Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences. https://arxiv.org/abs/1908.05123

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