Series for 1/π Using Legendre's Relation

2013/02/25 by Wan, James G.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1302.5984

Abstract

We present a new method for producing series for 1/π and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic K'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.

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