where μ is a nonnegative measure on [0,∞) such that the integral (2) converges for all x > 0. This means that a function f(x) is completely monotonic on (0,∞) if and only if it is a Laplace transform of the measure μ. The completely monotonic functions have applications in different branches of mathematical sciences. For example, they play some role in combinatorics, numerical and asymptotic an...
