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

  • Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)
  • Received : 2021.07.23
  • Accepted : 2021.09.01
  • Published : 2021.11.30
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Abstract

In this paper, we use theta-function identities involving parameters 𝑙5,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.

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Acknowledgement

This work is supported by a research grant from the Busan National University of Education in 2021.

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