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The Rogers-Ramanujan continued fraction and a quintic iteration for
Author(s):
Heng Huat
Chan;
Shaun
Cooper;
Wen-Chin
Liaw
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3417-3424.
MSC (2000):
Primary 11Y60;
Secondary 11F20, 11F27, 33E05
Posted:
July 3, 2007
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Abstract:
Properties of the Rogers-Ramanujan continued fraction are used to obtain a formula for calculating with quintic convergence.
References:
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- 7.
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with Ramanujan's modular equations, Rocky Mountain J. Math. 19 (1989) 93-102. MR 1016163 (91a:11072) - 8.
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- 9.
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via the Dedekind eta function, in Organic Mathematics, J. Borwein, P. Borwein, L. Jörgenson and R. Corless, eds., American Mathematical Society, Providence, RI, 1997, pp. 89-115. MR 1483915 (98j:11030) - 10.
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, in Number Theory for the Millennium, I, M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand and W. Philipp, eds., A. K. Peters, Natick, MA, 2002, pp. 197-213. MR 1956226 (2003k:11194) - 11.
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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:
10.1090/S0002-9939-07-09031-4
PII:
S 0002-9939(07)09031-4
Received by editor(s):
December 9, 2005
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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