Convexity and Monotonicity Involving the Complete Elliptic Integral of the First Kind

Let K r be the complete elliptic integral of the first kind defined on 0 , 1 . By virtue of the auxiliary function H f , g = f ′ / g ′ g - f , we prove that the function Q p x = ln p / 1 - x K x is strictly convex on 0 , 1 if and only if 0 < p ≤ 4 , thus answering a conjecture. Moreover, we compl...

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Bibliographic Details

Published in:	Resultate der Mathematik Vol. 78; no. 1; p. 29
Main Authors:	Tian, Jing-Feng, Yang, Zhen-Hang
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.02.2023 Springer Nature B.V
Subjects:	Convexity Mathematics Mathematics and Statistics inequality Primary 33C05 26A51 Secondary 39B62 hypergeometric function convexity Complete elliptic integral of the first kind
ISSN:	1422-6383, 1420-9012
Online Access:	Get full text
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