Formula:803

Digital Library of Mathematical Functions ID 2.6.E8

${\displaystyle{\displaystyle\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)=\int_{0}^{\infty}\frac{f(t)}{t+z}\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Stieltjes transform
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle f(t)}}$: locally integrable function
 

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