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

Paek, Dae Hyun; Paek, Dae Hyun

doi:https://doi.org/10.7468/jksmeb.2021.28.4.377

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P-ISSN3059-0604
E-ISSN3059-1309
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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: 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

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, 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 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.

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

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Article Contents

Vol.28 No.4

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

Abstract

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