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

Paek, Dae Hyun; Paek, Dae Hyun; Shin, Yong Jin; Shin, Yong Jin; Yi, Jinhee; Yi, Jinhee

doi:10.7468/jksmeb.2018.25.1.17

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P-ISSN3059-0604
E-ISSN3059-1309
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Vol.25 No.1

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

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

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

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

Paek, Dae Hyun
Shin, Yong Jin
Yi, Jinhee

Paek,, D. H. , Shin,, Y. J. , & Yi,, J. (2018). ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY MODULAR EQUATIONS OF DEGREE 3, 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 $G(e^{-{\pi}\sqrt{n}})$ 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

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Article Contents

Vol.25 No.1

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

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics