\[\mathcal{H}\left(f\right)\left(x\right)=\mathcal{H}\mskip-3.0muf\mskip 3.0mu%
\left(x\right)=\frac{1}{\pi}\pvint^{\infty}_{-\infty}\frac{f(t)}{t-x}\,\mathrm%
{d}t,\]