Chudnovsky-Ramanujan Type Formulae for the Legendre Family

TL;DR

This paper derives new formulas for calculating 1/π using hypergeometric functions related to the Legendre family of elliptic curves, extending classical results with novel identities.

Contribution

It introduces Chudnovsky-Ramanujan type formulas specifically for the Legendre family, expanding the scope of such identities beyond classical elliptic curves.

Findings

Derived two new identities for 1/π involving hypergeometric functions

Extended classical formulas to the Legendre family of elliptic curves

Validated the formulas through mathematical proofs

Abstract

We apply the method established in our previous work to derive a Chudnovsky-Ramanujan type formula for the Legendre family of elliptic curves. As a result, we prove two identities for $1/\pi$ in terms of hypergeometric functions.