Stieltjes transformation

In mathematics, the Stieltjes transformation S_ρ(z) of a measure of density ρ on a real interval I is the function of the complex variable z defined outside I by the formula

$${\displaystyle S_{\rho }(z)=\int _{I}{\frac {\rho (t)\,dt}{t-z}},\qquad z\in \mathbb {C} \setminus I.}$$