Monotonicity and inequalities for the gamma function.

In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function is strictly increasing from $( 0,\infty ) $ onto $( 1,1860/343 ) $ . This not only yields some known and new inequalities for the gamma function, but also gives some completely monotonic functions related to the gamma function. [ABSTRACT FROM AUTHOR]