# FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION

• Qi, Feng (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HENAN UNIVERSITY, RESEARCH INSTITUTE OF MATHEMATICAL INEQUALITY THEORY HENAN POLYTECHNIC UNIVERSITY) ;
• Niu, Da-Wei (COLLEGE OF INFORMATION AND BUSINESS ZHONGYUAN UNIVERSITY OF TECHNOLOGY) ;
• Cao, Jian (DEPARTMENT OF MATHEMATICS EAST CHINA NORMAL UNIVERSITY) ;
• Chen, Shou-Xin (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HEHAN UNIVERSITY)
• Published : 2008.03.31

#### Abstract

In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in $(-\frac{1}{2},\infty)$ or $(0,\infty)$; some inequalities involving the classical Euler gamma function are deduced and compared with those originating from certain problems of traffic flow, due to J. Wendel and A. Laforgia, and relating to the well known Stirling's formula.

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