Ramanujan-like series for 1/π² and String Theory

2010/09/27 by Gert Almkvist, Almkvist, Gert, Jesús Guillera +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1009.5202

openalex publication_date 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the machinery from the theory of Calabi-Yau differential equations, we find formulas for 1/π² of hypergeometric and non-hypergeometric types.

Citations

• Transformations of Jesus Guillera's formulas for 1/Pi²
• List of conjectural series for powers of π and other constants

Cited by

• Bilateral sums related to Ramanujan-like series
• More hypergeometric identities related to Ramanujan-type series
• Ramanujan-Sato-like series

Related

• A new Ramanujan-like series for 1/π²
• Ramanujan-Sato-like series
• A Matrix form of Ramanujan-type series for 1/π
• More hypergeometric identities related to Ramanujan-type series
• A General Method for Constructing Ramanujan Formulas for 1/π^ν