High accuracy asymptotic bounds for the complete elliptic integral of the second kind

In the article, we prove that the double inequality pi/2J(r') - 51 pi-160/160 r(16) < epsilon(r) < pi/2(r') - 5 pi/3x2(31) r(16) holds for all r is an element of (0, 1), where epsilon(r) = integral(0) (pi/2)root 1-r(2)sin(2)(t)dt is the complete elliptic integral of the second kind, r' = (1 - r(2))(1/2) and J(r) = 51r(2) + 20r root r + 50r + 20 root r + 51/16(5r + 2 root r + 5). (C) 2018 Elsevier Inc. All rights reserved.