Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Jinhee Yi (2001)
Acta Arithmetica
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Jinhee Yi (2001)
Acta Arithmetica
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Baruah, Nayandeep Deka, Saikia, Nipen (2006)
International Journal of Mathematics and Mathematical Sciences
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Avner Ash, Lee Rudolph (1979)
Inventiones mathematicae
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M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)
Open Mathematics
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In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.
David Grant (2002)
Acta Arithmetica
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B.C. Berndt, H.H. Chan, L.-C. Zhang (1996)
Journal für die reine und angewandte Mathematik
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Masri, Riad, Ono, Ken (2009)
International Journal of Mathematics and Mathematical Sciences
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Koruoğlu, Özden (2010)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Seung Hwan Son (2001)
Acta Arithmetica
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(2013)
Acta Arithmetica
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The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.
Dennis Johnson, John J. Millson (1990)
Inventiones mathematicae
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Heng Huat Chan, Kok Ping Loo (2007)
Acta Arithmetica
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Hiroyuki Yoshida (1984)
Journal für die reine und angewandte Mathematik
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D. Choi (2006)
Acta Arithmetica
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K. Ramanathan (1990)
Acta Arithmetica
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