特殊拟算术平均的单参数调和与几何平均确界

Optimal Bounds for Special Quasi arithmetic Mean in Terms of One parameter Harmonic and Geometric Means

运用单调性罗必塔法则和实分析方法,通过建立一个特殊拟算术平均关于单参数调和平均及单参数几何平均的最优不等式,得到一个第一类完全椭圆积分的确界,所得结果是已知结论的改进.

By using the monotone of L’Hopital’s rule and the method of real analysis,establishing a special quasi arithmetic mean of the optimal inequalities with respect to the one parameter harmonic and geometric means,an exact bound of the first class of complete elliptic integrals is obtained.The results are the improvement of the previously known results.