Monotonicity and convexity involving generalized elliptic integral of the first kind

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 115; no. 2
• Main Authors: Zhao, Tie-Hong, Wang, Miao-Kun, Chu, Yu-Ming
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Concavity; Convexity; Integrals; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Original Paper; Theoretical; Upper bounds; Ramanujan constant; Generalized elliptic integral; Convexity; 33E05; Monotonicity; 33C05

In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind K a ( r ) and its approximation log [ 1 + 2 / ( a r ′ ) ] , and also the convexity (concavity) of their difference for a ∈ ( 0 , 1 / 2 ] . As an application, we give new bounds...