Rational Hypergeometric Ramanujan Identities for $1/\pi^c$: Survey and Generalizations

TL;DR

This paper provides a unified proof for all known rational hypergeometric Ramanujan identities for 1/π and surveys various generalizations including identities for 1/π^c, Taylor expansions, upside-down formulas, and supercongruences.

Contribution

It offers a simple, unified proof for existing identities and compiles a comprehensive survey of their generalizations without proofs.

Findings

Unified proof for all rational hypergeometric Ramanujan identities for 1/π

Survey of generalizations including identities for 1/π^c and supercongruences

Compilation of various related formulas and expansions

Abstract

We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for $1/\pi$, and give a complete survey (without proof) of several generalizations: rational hypergeometric identities for $1/\pi^c$, Taylor expansions, upside-down formulas, and supercongruences.