• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.377-386
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• 2021

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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권3호
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• pp.245-254
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• 2022

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

• East Asian mathematical journal
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• 제31권5호
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• pp.659-665
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• 2015

Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.

• 대한수학회지
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• 제47권2호
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• pp.223-233
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• 2010

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

• 대한수학회보
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• 제59권1호
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• pp.15-25
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• 2022

In 1963, Graham introduced a problem to find integer partitions such that the reciprocal sum of their parts is 1. Inspired by Graham's work and classical partition identities, we show that there is an integer partition of a sufficiently large integer n such that the reciprocal sum of the parts is 1, while the parts satisfy certain congruence conditions.