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http://dx.doi.org/10.7468/jksmeb.2016.23.3.223

ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9  

PAEK, DAE HYUN (DEPARTMENT OF MATHEMATICS EDUCATION, BUSAN NATIONAL UNIVERSITY OF EDUCATION)
YI, JINHEE (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, KOREA SCIENCE ACADEMY OF KAIST)
Publication Information
The Pure and Applied Mathematics / v.23, no.3, 2016 , pp. 223-236 More about this Journal
Abstract
We show how to evaluate the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for n = 4m, 4−m, 2 · 4m, and 2−1 · 4−m for some nonnegative integer m by using modular equations of degree 9. We then find some explicit values of them.
Keywords
continued fraction; modular equations; theta functions;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
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