Formula:504

Digital Library of Mathematical Functions ID 1.14.E43

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

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
 

Resources that cite this formula

No records found.