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Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals
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Journal Article
Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals
2023
Overview
In the article, we prove that the inequalities Hp(K(r),ℰ(r))>π2,Lq(K(r),ℰ(r))>π2 hold for all r ∈ (0, 1) if and only if p ≥ −3/4 and q ≥ −3/4, where Hp(a, b) and Lq(a, b) are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b, and K(r) and ℰ(r) are respectively the complete elliptic integrals of the first and second kinds.
Publisher
Springer Nature B.V
Subject
