Series for $1/\pi$ Using Legendre's Relation
Number Theory
2013-02-26 v1
Abstract
We present a new method for producing series for and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic '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.
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}
}