%0 Journal Article %T Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind %A Yang, Zhen-Hang %A Chu, Yu-Ming %A Zhang, Xiao-Hui %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 3 %@ ISSN 2008-1901 %F Yang2017 %X In the article, we prove that the double inequality \[25/16<\varepsilon(r)/S_{5/2,2}(1,\acute{r})<\pi/2,\] holds for all \(r \in (0, 1)\) with the best possible constants \(25/16\) and \(\pi/2\), where \(\acute{r}=(1-r^2)^{1/2}, \varepsilon(r)=\int^{\pi/2}_0\sqrt{1-r^2\sin^2(t)}dt\) , is the complete elliptic integral of the second kind and \(S_{p,q}(a,b)=[q(a^p-b^p)/(p(a^q-b^q))]^{1/(p-q)}\), is the Stolarsky mean of a and b. %9 journal article %R 10.22436/jnsa.010.03.06 %U http://dx.doi.org/10.22436/jnsa.010.03.06 %P 929--936