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

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.

References in corpus (3)

• History of the formulas and algorithms for pi
• Kind of proofs of Ramanujan-like series
• Some conjectured formulas for 1/Pi coming from polytopes, K3-surfaces and Moonshine