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

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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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: 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

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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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 <TEX>$G(e^{-{\pi}\sqrt{n}})$</TEX> and <TEX>$G(-e^{-{\pi}\sqrt{n}})$</TEX> for n = 4m, 4−m, 2 · 4m, 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: The Pure and Applied Mathematics