  The Coulomb-gauge vector potential of a uniformly moving point charge is
obtained by calculating the gauge function for the transformation between the
Lorenz and Coulomb gauges. The expression obtained for the difference between
the vector potentials in the two gauges is shown to satisfy a Poisson equation
to which the inhomogeneous wave equation for this quantity can be reduced. The
right-hand side of the Poisson equation involves an important but easily
overlooked delta-function term that arises from a second-order partial
derivative of the Coulomb potential of a point charge.
