A family of Ramanujan–Orr formulas for 1/π

DOI10.1080/10652469.2015.1021799zbMath1432.33014arXiv1501.06413OpenAlexW2962867498MaRDI QIDQ5262271

Jesús Guillera

Publication date: 13 July 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06413

zbMATH Keywords

hypergeometric seriescomplete elliptic integralZeilberger's algorithmLegendre's relationRamanujan-Orr type formulas

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Elliptic integrals as hypergeometric functions (33C75) Software, source code, etc. for problems pertaining to special functions (33-04)

Related Items (2)

A method for proving Ramanujan's series for \(1/\pi\) ⋮ Short Walk Adventures

Cites Work

• Series for 1/π using Legendre's relation
• Algebraic Transformations of Gauss Hypergeometric Functions
• About a New Kind of Ramanujan-Type Series
• Ramanujan-like Series for 1/π²and String Theory
• A generalization of a Brafman-Bailey type identity

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