Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind

In the article, we prove that the double inequality 25/16 < epsilon(r)/S-5/2,S-2 (1, r ') < pi/2, holds for all r is an element of(0, 1) with the best possible constants 25/16 and pi/2, where r ' = (1 - r(2))(1/2),epsilon(r) = integral(pi/2)(0) root 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. (C) 2017 All rights reserved.