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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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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: The Pure and Applied Mathematics / 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
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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(1), 17-29, https://doi.org/10.7468/jksmeb.2018.25.1.17

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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