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http://dx.doi.org/10.7468/jksmeb.2018.25.1.17

ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY MODULAR EQUATIONS OF DEGREE 3  

Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)
Shin, Yong Jin (Department of Mechanical and Aerospace Engineering, Seoul National University)
Yi, Jinhee (Department of Mathematics and Computer Science, Korea Science Academy of KAIST)
Publication Information
The Pure and Applied Mathematics / v.25, no.1, 2018 , pp. 17-29 More about this Journal
Abstract
We find modular equations of degree 3 to evaluate some new values of the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for $n={\frac{2{\cdot}4^m}{3}}$, ${\frac{1}{3{\cdot}4^m}}$, and ${\frac{2}{3{\cdot}4^m}}$, where m = 1, 2, 3, or 4.
Keywords
continued fraction; modular equation; theta function;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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