  Persson's theory of contact is extensively used in the study of the purely
normal interaction between a nominally flat rough surface and a rigid flat. In
the literature, Persson's theory was successfully applied to the elastoplastic
contact problem with a scale-independent hardness $H$. However, it yields a
closed-form solution, $P(p, \xi)$, in terms of an infinite sum of sines. In
this study, $P(p, \xi)$ is found to have a simpler form which is a
superposition of three Gaussian functions. A rigorous proof of the boundary
condition $P(p=0, \xi)=P(p=H, \xi) = 0$ is given based on the new solution.
