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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2018, v.25 no.1, pp.17-29

https://doi.org/10.7468/jksmeb.2018.25.1.17

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)

Paek, Dae Hyun, Shin, Yong Jin, & Yi, Jinhee. (2018). ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY MODULAR EQUATIONS OF DEGREE 3. 한국수학교육학회지시리즈B:순수및응용수학, 25(1), 17-29, https://doi.org/10.7468/jksmeb.2018.25.1.17

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Abstract

We find modular equations of degree 3 to evaluate some new values of the cubic continued fraction <TEX>$G(e^{-{\pi}\sqrt{n}})$</TEX> and <TEX>$G(-e^{-{\pi}\sqrt{n}})$</TEX> for <TEX>$n={\frac{2{\cdot}4^m}{3}}$</TEX>, <TEX>${\frac{1}{3{\cdot}4^m}}$</TEX>, and <TEX>${\frac{2}{3{\cdot}4^m}}$</TEX>, where m = 1, 2, 3, or 4.

keywords: continued fraction, modular equation, theta function

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논문 상세

Vol.25 No.1

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

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학