Sharp Generalized Seiffert Mean Bounds for Toader Mean

Abstract EN

For p∈[0,1], the generalized Seiffert mean of two positive numbers a and b is defined by Sp(a,b)=p(a-b)/arctan[2p(a-b)/(a+b)], 0

In this paper, we find the greatest value α and least value β such that the double inequality Sα(a,b)0 with a≠b, and give new bounds for the complete elliptic integrals of the second kind.

Here, T(a,b)=(2/π)∫0π/2a2cos2θ+b2sin2θdθ denotes the Toader mean of two positive numbers a and b.