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ISSN : 1226-0657

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Vol.28 No.4
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EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES

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
2021, v.28 no.4, pp.377-386
https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.377
Paek, Dae Hyun
Paek,, D. H. (2021). EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(4), 377-386, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.4.377
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Abstract

In this paper, we use theta-function identities involving parameters &#x1D459;<sub>5,n</sub>, &#x1D459;'<sub>5,n</sub>, and &#x1D459;'<sub>5,4n</sub> to evaluate the Rogers-Ramanujan continued fractions <TEX>$R(e^{-2{\pi}{\sqrt{n/20}}})$</TEX> and <TEX>$S(e^{-{\pi}{\sqrt{n/5}}})$</TEX> for some positive rational numbers n.

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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