Series for 1/π Using Legendre's Relation

الأصل · EN

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.