On generalized Stieltjes functions

Stamatis Koumandos, Henrik L. Pedersen

It is shown that a function $f$ is a generalized Stieltjes function of order $\lambda >0$ if and only if $x^{1-\lambda }(x^{\lambda -1+k}f(x){)}^{(k)}$ is completely monotonic for all $k\ge 0$, thereby…