논문KCI 등재
Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited
한국수학교육학회|2022.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제29권 제3호|pp. 245-254
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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 $n=\frac1{5 \cdot 4^m}$ and $\frac1{4^m}$, where $m$ is any positive integer. We give some explicit evaluations of them.
Abstract
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 $n=\frac1{5 \cdot 4^m}$ and $\frac1{4^m}$, where $m$ is any positive integer. We give some explicit evaluations of them.
참고문헌 (17)
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