  It is known that Newton's law of gravity holds asymptotically on a flat
"brane" embedded in an anti-de Sitter "bulk" ; this was shown not only when
gravity in the bulk is described by Einstein's theory but also in Einstein
"Lanczos Lovelock Gauss-Bonnet"'s theory. We give here the expressions for the
corrections to Newton's potential in both theories, in analytic form and valid
for all distances. We find that in Einstein's theory the transition from the
1/r behaviour at small r to the 1/r^2 one at large r is quite slow. In the
Einstein Gauss-Bonnet case on the other hand, we find that the correction to
Newton's potential can be small for all r. Hence, Einstein Gauss-Bonnet
equations in the bulk (rather than simply Einstein's) induce on the brane a
better approximation to Newton's law.
