Cauchy principal value

Examples

$\mathcal{P}\int_{-\infty}^\infty dx\, \frac{f(x)}{x-a}\,$

$= \lim_{\epsilon \to 0^+} \left[\int_{-\infty}^{a-\epsilon} dx\, \frac{f(x)}{x-a} + \int_{a+\epsilon}^\infty dx\, \frac{f(x)}{x-a} \right]\,$ .