Self-replication and Borwein-like algorithms

DOI10.1007/s11139-017-9927-0zbMath1456.11238arXiv1702.05378OpenAlexW2749387306MaRDI QIDQ1623892

Jesús Guillera

Publication date: 15 November 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05378

zbMATH Keywords

hypergeometric seriesalgebraic transformationsBorwein-type algorithms

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Numerical approximation and evaluation of special functions (33F05) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Elliptic integrals as hypergeometric functions (33C75)

Uses Software

• FXT
• hfloat

Cites Work

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• Pi: The Next Generation
• Ramanujan's Theta Functions
• Easy Proofs of Some Borwein Algorithms for π
• Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• Matters Computational
• A Cubic Counterpart of Jacobi's Identity and the AGM
• New proofs of Borwein-type algorithms for Pi

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