  We analyze the possible expansions of the interatomic potential
$U(|\textbf{r}_{1}-\textbf{r}_{2}|)$ in a Fourier series for a cyclic system
and a system with boundaries. We also study the transition from exact
expansions for a finite system to the expansion that is commonly used in the
thermodynamic limit. The analysis shows that such a transition distorts the
potential of a bounded system by making it cyclic.
