It is commonly defined the ratio
$$R(s)= \frac{\sigma(e^+e^-\longrightarrow \textrm{hadrons}; s)}{\sigma(e^+e^-\longrightarrow \mu^+\mu^-;s)}$$ where $s$ is the center-of-mass energy squared. I found in many references that $$ R(s)= \frac{1}{2i\pi} \lim_{\varepsilon \rightarrow 0^+} \left[ \Pi(s+i\varepsilon)- \Pi(s-i\varepsilon) \right] $$ where $\Pi(q^2)$ is the vacuum polarization function. How is the proof of this made?
