ANSWERS TO THREE CONJECTURES ON CONVEXITY OF THREE FUNCTIONS INVOLVING COMPLETE ELLIPTIC INTEGRALS OF THE FIRST KIND

Wang, MK; Chu, HH; Li, YM; Chu, YM

Chu, YM (corresponding author), Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.; Chu, YM (corresponding author), Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2020; 14 (1): 255

Abstract

In the article, we prove that the function x -> (1-x)K-P(root x) is logarithmically concave on (0, 1) if and only if p >= 7/32, the function x -......

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