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arXiv · 1206.5494

Sharp bounds for the second Seiffert mean in terms of power means

Zhen-Hang Yang
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Abstract

For a,b>0 with a\not=b, let T(a,b) denote the second Seiffert mean defined by T(a,b)=((a-b)/(2arctan((a-b)/(a+b)))) and A_{r}(a,b) denote the r-order power mean. We present the sharp bounds for the second Seiffert mean in terms of power means: A_{p_1}(a,b)<T(a,b)\leqA_{p_2}(a,b), where p_1= log_{π/2}2 and p_2=5/3 can not be improved.

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Zhen-Hang Yang. 2012-06-24. Sharp bounds for the second Seiffert mean in terms of power means. https://arxiv.org/abs/1206.5494

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