Abstract
In the article, we present several monotonicity theorems and inequalities for the modular equation functions $$m_{a}(r)$$ and $$\mu _{a}(r),$$ and find the infinite-series formulas for $$m_{1/3}(r)$$ and $$m_{1/4}(r)$$ which depend only on r. As applications, we find several precise explicit estimates for the solution of Ramanujan’s generalized modular equation.
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