The Rogers-Ramanujan continued fraction and a quintic iteration for 1/𝜋

Chan, Heng Huat; Cooper, Shaun; Liaw, Wen-Chin

doi:10.1090/S0002-9939-07-09031-4

The Rogers-Ramanujan continued fraction and a quintic iteration for $1/\pi$

Authors: Heng Huat Chan, Shaun Cooper and Wen-Chin Liaw
Journal: Proc. Amer. Math. Soc. 135 (2007), 3417-3424
MSC (2000): Primary 11Y60; Secondary 11F20, 11F27, 33E05
DOI: https://doi.org/10.1090/S0002-9939-07-09031-4
Published electronically: July 3, 2007
MathSciNet review: 2336553
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Abstract: Properties of the Rogers-Ramanujan continued fraction are used to obtain a formula for calculating $1/\pi$ with quintic convergence.

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Additional Information

Heng Huat Chan
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Email: matchh@nus.edu.sg

Shaun Cooper
Affiliation: Institute of Information and Mathematical Sciences, Massey University–Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand
Email: s.cooper@massey.ac.nz

Wen-Chin Liaw
Affiliation: Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi 621, Taiwan, Republic of China
Email: wcliaw@math.ccu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-07-09031-4
Received by editor(s): December 9, 2005
Published electronically: July 3, 2007
Additional Notes: The third author is grateful for the support from the National Science Council of Taiwan, Republic of China, through Grant NSC95-2115-M-194-012.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.