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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics and Computer Science, Korea Science Academy of KAIST)
Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)

Yi, Jinhee, & Paek, Dae Hyun. (2022). EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES REVISITED. 한국수학교육학회지시리즈B:순수및응용수학, 29(3), 245-254, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.3.245

복사

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

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논문 상세

Vol.29 No.3

EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES REVISITED

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학