Stieltjes transformation
In mathematics, the Stieltjes transformation Sρ(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 S ρ ( z ) = ∫ I ρ ( t ) d t t − z , z ∈ C ∖ I . {\displaystyle S_{\rho }(z)=\int _{I}{\frac {\rho (t)\,dt}{t-z}},\qquad z\in \mathbb {C} \setminus I.} == Inverse formula == Under certain conditions we can reconstitute the density function ρ starting from its Stieltjes transformation thanks to the inverse formula of Stieltjes–Perron.