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

한국수학교육학회지시리즈B:순수및응용수학 / 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

이진희 (한국과학영재학교)
안지원 (한국과학영재학교)
이강훈 (한국과학영재학교)
백대현 (부산교육대학교)

이진희, 안지원, 이강훈, & 백대현. (2024). . 한국수학교육학회지시리즈B:순수및응용수학, 31(2), 189-200, https://doi.org/10.7468/jksmeb.2024.31.2.189

복사

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.

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Vol.31 No.2

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학