Formula_13126

\[(\delta(x), \varphi(x))=\varphi(0)=\lim _{\varepsilon \rightarrow+0} \frac{1}{\pi} \int \frac{\varepsilon}{x^{2}+\varepsilon^{2}} \varphi(x) d x, \quad \varphi \in D\left(\mathbb{R}^{1}\right) .\]