English

The fastest series for $1/\pi$ due to Ramanujan. Proofs from modular polynomials

Number Theory 2025-07-21 v13

Abstract

First we give general formulas for proving real or complex Ramanujan series for 1/π1/\pi. Then, as an example, we apply them for providing complete proofs of the fastest series for 1/π1/\pi due to Ramanujan using Russell and Weber modular polynomials. We recommend the reader to use a Maple program which is in the web of the author for automatically proving any Ramanujan-type series for 1/π1/\pi.

Keywords

Cite

@article{arxiv.1911.03968,
  title  = {The fastest series for $1/\pi$ due to Ramanujan. Proofs from modular polynomials},
  author = {Jesús Guillera},
  journal= {arXiv preprint arXiv:1911.03968},
  year   = {2025}
}

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14 pages