Abstract:

The function [image omitted] for x > 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function [image omitted] for a ∈  and t ∈ (0, ∞) is verified. The possible origin and background of the function (*) are revealed to be related to [image omitted] the remainder of Binet's formula. Some applications of above results to the difference of θ(x) are noted.

Keywords: monotonicity; logarithmic concavity; exponential function; inequality; origin; Binet's formula

Document Type: Research article

DOI: 10.1080/00207390801986841

Affiliations: 1: Department of Mathematics, Sanmenxia Polytechnic, Sanmenxia City, Henan Province 472000, China 2: Department of Mathematics, Zhengzhou Teachers College, Zhengzhou City, Henan Province 450044, China 3: School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China 4: Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China