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

Yi, Jinhee; Yi, Jinhee; Paek, Dae Hyun; Paek, Dae Hyun

doi:https://doi.org/10.7468/jksmeb.2022.29.3.245

P-ISSN3059-0604
E-ISSN3059-1309
KCI

Home

OA Policy

ISSN : 3059-0604

Article Contents

e-Submission

Vol.29 No.3

Citation Share

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

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

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. , 29(3), 245-254, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.3.245

copy

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

바로가기메뉴

Article Contents

Vol.29 No.3

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

Abstract

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