The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES REVISITED

  • Yi, Jinhee (Department of Mathematics and Computer Science, Korea Science Academy of KAIST) ;
  • Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)
  • Received : 2022.04.12
  • Accepted : 2022.06.26
  • Published : 2022.08.31
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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 $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

Keywords

Acknowledgement

This work was supported by the Korea Science Academy of KAIST with funds from the Ministry of Science and ICT.

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