Hypergeometric modular equations

TL;DR

This paper documents 1192 functional identities involving hypergeometric modular equations, which are useful for deriving Ramanujan-type formulas for 1/π and computing mathematical constants.

Contribution

It presents a large collection of hypergeometric modular identities, expanding tools for mathematical analysis and constant computation.

Findings

1192 functional identities recorded

Applications in Ramanujan-type formulas for 1/π

Useful for constant computation

Abstract

We record $$ \binom{42}2+\binom{23}2+\binom{13}2=1192 $$ functional identities that, apart from being amazingly amusing by themselves, find applications in derivation of Ramanujan-type formulas for $1/\pi$ and in computation of mathematical constants.