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中文摘要：
文中主要运用单调性L’Hopital法则等分析工具探讨了由广义椭圆积分所定义的组合函数的单调性，及与一些初等函数组合的单调性，并由此获得其精确不等式．同时，推广了广义椭圆积分的相关已知结果，这些结果有助于广义Grotzsch环函数和广义Ramanuian模方程及其解的研究．
英文摘要：
Some monotonicity properties of certain combinations of these functions defined in terms of the generalized elliptic integrals and some elementary functions are mainly obtained by monotone L＇ Hopital rule, and from which some precise inequalities are obtained. Meanwhile, some known results are generalized for the generalized elliptic integrals, these results will be used to study the generalized Grotzsch ring function, Ramanujan＇ s modular equations and the solutions of them.
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