Extension of a complete monotonicity theorem with applications

Zhen-Hang Yang

Let $F_p(x)=L(t^{p}f(t))={\int }_0^{\infty }{t}^{p}f(t)e^{-xt}dt$ converge on $(0,\infty )$ for $p\in {\mathbb{N}}_0=\mathbb{N}\cup 0$, where $f(t)$ is positive on $(0,\infty )$.…