What is the procedure to find the weight function $p(t)$ of a Stieltjes integral $F(x)=\int_0^\infty p(t)/(1+xt)dt$ such that $F(x)=\sum_{n=0}^\infty a_n (-x)^n$ and $a_n=\int_0^\infty t^n p(t)dt$?
For example, I know that $F(x)=log(1+x)/x$ is a Stieltjes function, how do I find $p(t)$?
Note: Bender & Orszag seem to me to have neglected to give an easy anser to this question in their book.
