Bull. Korean Math. Soc. 2013; 50(4): 1221-1233
Printed July 1, 2013
https://doi.org/10.4134/BKMS.2013.50.4.1221
Copyright © The Korean Mathematical Society.
Dae Hyun Paek and Jinhee Yi
Busan National University of Education, Korea Science Academy of KAIST
We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and formulas for the parameterizations for the theta functions $\varphi$ and $\psi$. In addition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.
Keywords: theta functions, modular equations, continued fractions
MSC numbers: Primary 11F27, 33C90; Secondary 11F20, 33C05, 33C75
2013; 50(4): 1315-1328
2015; 52(1): 263-273
2013; 50(3): 761-776
2014; 51(1): 157-171
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