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ISSN : 1226-0657

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Vol.31 No.2

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On Evaluations of the Cubic Continued Fraction by Modular Equations of Degree 3 Revisited

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
2024, v.31 no.2, pp.189-200
https://doi.org/10.7468/jksmeb.2024.31.2.189
Jinhee Yi
Ji Won Ahn
Gang Hun Lee
Paek Dae Hyun
Jinhee, Y. , Ji, W. A. , Gang, H. L. , & Paek, D. H. (2024). On Evaluations of the Cubic Continued Fraction by Modular Equations of Degree 3 Revisited. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 31(2), 189-200, https://doi.org/10.7468/jksmeb.2024.31.2.189

Abstract

We derive modular equations of degree 3 to find corresponding thetafunction identities. We use them to find some new evaluations of G(e^-π√n ) and G(e^-π√n ) for n= {25} over {3 BULLET 4 ^{m-1}} and {4^1-m} over {3 BULLET 25}, where m = 0, 1, 2.

keywords
continued fractions, modular equations, theta-function identities.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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