Formula:1273

Digital Library of Mathematical Functions ID 3.5.E46

${\displaystyle{\displaystyle\mathcal{H}\mskip-3.0mu f\mskip 3.0mu \left(x\right)=\frac{1}{\pi}\pvint_{-\infty}^{\infty}\frac{f(t)}{t-x}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle x\in\mathbb{R}}}$

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
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}$: Cauchy principal value
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
 

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