English

Series for $1/\pi$ Using Legendre's Relation

Number Theory 2013-02-26 v1

Abstract

We present a new method for producing series for 1/π1/\pi and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic KK's; this way we avoid much of modular theory or creative telescoping. Many of our series involve special values of Legendre polynomials; their relationship to the more traditional Ramanujan series is discussed.

Keywords

Cite

@article{arxiv.1302.5984,
  title  = {Series for $1/\pi$ Using Legendre's Relation},
  author = {James G. Wan},
  journal= {arXiv preprint arXiv:1302.5984},
  year   = {2013}
}
R2 v1 2026-06-21T23:31:52.905Z