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http://dx.doi.org/10.7468/jksmeb.2022.29.3.245

EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES REVISITED  

Yi, Jinhee (Department of Mathematics and Computer Science, Korea Science Academy of KAIST)
Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)
Publication Information
The Pure and Applied Mathematics / v.29, no.3, 2022 , pp. 245-254 More about this Journal
Abstract
In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.
Keywords
theta-function; modular equation; theta-function identity; Rogers-Ramanujan continued fraction;
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Times Cited By KSCI : 1  (Citation Analysis)
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