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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics Education, Busan National University of Education)

Paek, Dae Hyun. (2021). EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES. 한국수학교육학회지시리즈B:순수및응용수학, 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 𝑙5,n, 𝑙'5,n, and 𝑙'5,4n 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

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논문 상세

Vol.28 No.4

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

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학