  A detailed theoretical derivation of the cross sections of $e^+e^- \to
e^+e^-$ and $e^+e^- \to \mu^+\mu^-$ around the $J/\psi$ resonance is reported.
The resonance and interference parts of the cross sections, related to $J/\psi$
resonance parameters, are calculated. Higher-order corrections for vacuum
polarization and initial-state radiation are considered. An arbitrary upper
limit of radiative correction integration is involved. Full and simplified
versions of analytic formulae are given with precision at the level of 0.1% and
0.2%, respectively. Moreover, the results obtained in the paper can be applied
to the case of the $\psi(3686)$ resonance.
