Formula:503

Digital Library of Mathematical Functions ID 1.14.E42

${\displaystyle{\displaystyle\mathcal{H}\mskip-3.0mu f\mskip 3.0mu \left(x\right)=\lim_{y\to 0+}\frac{1}{\pi}\int^{\infty}_{-\infty}\frac{t-x}{(t-x)^{2}+y^{2}}f(t)\mathrm{d}t,}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
 

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