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ISSN : 1226-0657

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Vol.29 No.3

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Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited

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
2022, v.29 no.3, pp.245-254
https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.3.245
Yi, Jinhee
Paek, Dae Hyun
Yi,, J. , & Paek,, D. H. (2022). Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 29(3), 245-254, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.3.245

Abstract

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R(<TEX>$e^{-2{\pi}\sqrt{n}}$</TEX>) and S(<TEX>$e^{-{\pi}\sqrt{n}}$</TEX>) for <TEX>$n=\frac{1}{5.4^m}$</TEX> and <TEX>$\frac{1}{4^m}$</TEX>, where m is any positive integer. We give some explicit evaluations of them.

keywords
theta-function, modular equation, theta-function identity, Rogers-Ramanujan continued fraction

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

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