Journal of the
Korean Mathematical Society JKMS

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 $\bigl(-\frac12,\infty\bigr)$ 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.

Keywords: logarithmically completely monotonic function, completely monotonic function, ratio of the gamma functions, Kershaw's inequality, Laforgia's inequality, Stirling's formula, Wendel's inequality

MSC numbers: Primary 33B15, 26A48, 26A51; Secondary 26D20