Sharp bounds for the second Seiffert mean in terms of power means

2012/06/24 by Zhen-Hang Yang, Yang, Zhen-Hang
Mathematics · #26D05 (Primary) 26A48 (Secondary) #26E60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A48 #msc:26D05 #msc:26E60

paper · pdf · doi:10.48550/arxiv.1206.5494

10 pages

arxiv created 2012/06/24 · arxiv updated 2012/06/26

Abstract

For a,b>0 with a\not=b, let T(a,b) denote the second Seiffert mean defined by T(a,b)=((a-b)/(2arctan((a-b)/(a+b)))) and A_r(a,b) denote the r-order power mean. We present the sharp bounds for the second Seiffert mean in terms of power means: A_p1(a,b)<T(a,b)\leqA_p2(a,b), where p₁= log_π/22 and p₂=5/3 can not be improved.

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