# ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II

• Published : 2013.07.31
• 40 4

#### Abstract

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

#### References

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#### Cited by

1. ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1315

#### Acknowledgement

Supported by : Busan National University