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

Jesús Guillera

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

Number Theory 2019-08-15 v1

Authors: Jesús Guillera

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.

Keywords

ramanujan-like series bilateral series negative powers of pi supercongruences hypergeometric identities number theory

Cite

@article{arxiv.1908.05123,
  title  = {Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences},
  author = {Jesús Guillera},
  journal= {arXiv preprint arXiv:1908.05123},
  year   = {2019}
}

Comments

18 pages

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

Abstract

Keywords

Cite

Comments

Related papers