Formula:510

Digital Library of Mathematical Functions ID 1.14.E49

${\displaystyle{\displaystyle\lim_{t\to 0+}\frac{\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(-\sigma-it\right)-\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(-\sigma+it\right)}{2\pi i}=\tfrac{1}{2}(f(\sigma+)+f(\sigma-)),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Stieltjes transform
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\sigma\in(a,b)}}$: parameter
 

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