On evaluations of the cubic continued fraction by modular equations of degree 9

PAEK, DAE HYUN; PAEK, DAE HYUN; YI, JINHEE; YI, JINHEE

doi:10.7468/jksmeb.2016.23.3.223

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P-ISSN3059-0604
E-ISSN3059-1309
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Vol.23 No.3

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On evaluations of the cubic continued fraction by modular equations of degree 9

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

2016, v.23 no.3, pp.223-236

https://doi.org/10.7468/jksmeb.2016.23.3.223

PAEK, DAE HYUN
YI, JINHEE

PAEK,, D. H. , & YI,, J. (2016). On evaluations of the cubic continued fraction by modular equations of degree 9, 23(3), 223-236, https://doi.org/10.7468/jksmeb.2016.23.3.223

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Abstract

We show how to evaluate the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for n = 4^m, 4^−m, 2 · 4^m, 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

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Article Contents

Vol.23 No.3

On evaluations of the cubic continued fraction by modular equations of degree 9

Abstract

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