Korean J. Math.  Vol 27, No 4 (2019)  pp.1043-1059
DOI: https://doi.org/10.11568/kjm.2019.27.4.1043

Evaluations of the cubic continued fraction by some theta function identities

Jinhee Yi, Dae Hyun Paek

Abstract


In this paper, we use some theta function identities involving two parameters $h_{n,k}$ and $h'_{n,k}$ for the theta function $\varphi$ to establish new evaluations of Ramanujan's cubic continued fraction.

Keywords


cubic continued fraction, theta function identities, parameters for the theta function

Subject classification

11F27, 33C90, 11F20, 33C05, 33C75

Sponsor(s)

Korea Science Academy of KAIST with funds from the Ministry of Science and ICT

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References


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