  It is shown that the self inductance of a wire loop may be written as a curve
integral akin to the Neumann formula for the mutual inductance of two wire
loops. The only difference is that contributions where the two integration
variables get too close to each other must be excluded from the curve integral
and evaluated in detail. The contributions of these excluded segments depend on
the distribution of the current in the cross section of the wire. They add to a
simple constant proportional to the wire length. The error of the new
expression is of first order in the wire radius if there are sharp corners and
of second order in the wire radius for smooth wire loops.
