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- E-ISSN3059-1309
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ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9
On evaluations of the cubic continued fraction by modular equations of degree 9
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2016, v.23 no.3, pp.223-236
https://doi.org/10.7468/jksmeb.2016.23.3.223
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)
YI, JINHEE (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, KOREA SCIENCE ACADEMY OF KAIST)
PAEK, DAE HYUN,
&
YI, JINHEE.
(2016). ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9. , 23(3), 223-236, https://doi.org/10.7468/jksmeb.2016.23.3.223
Abstract
We show how to evaluate the cubic continued fraction <TEX>$G(e^{-{\pi}\sqrt{n}})$</TEX> and <TEX>$G(-e^{-{\pi}\sqrt{n}})$</TEX> for n = 4<sup>m</sup>, 4<sup>−m</sup>, 2 · 4<sup>m</sup>, and 2<sup>−1</sup> · 4<sup>−m</sup> 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