  The closed analytical expression for the Uehling potential is derived. The
Uehling potential describes the lowest-order correction on vacuum polarisation
in atomic and muon-atomic systems. We also derive the analytical formula for
the interaction potential between two electrically charged point particles
which includes correction to the vacuum polarisation, but has correct
asymptotic behaviour at larger $r$. Our three-term analytical formula for the
Uehling potential opens a new avenue in the study of the vacuum polarisation in
light atomic systems.
