# ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS I

• Published : 2013.05.31
• 49 9

#### Abstract

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

#### Keywords

theta functions;modular equations

#### References

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#### Cited by

1. ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1221
2. 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