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

In the article, we prove that the double inequality 25/16 E(r)/S5/2,2(1, rt) π/2, holds for all r ∈ (0, 1) with the best possible constants 25/16 and π/2, where rt = (1 − r²)1/2, E(r) = rπ/2 I − r² sin²(t)dt, is 01 the complete elliptic integral of the second kind and Sp,q(a, b) = [q(ap − bp)/(p(aq − bq))]1/(p−q), is the Stolarsky mean of a and b. Qc 2017 All rights reserved.