Generic Approximation of functions by their pad\'{e} approximants, II

In \cite{5} we proved that generically functions defined in any open set can be approximated by a sequense of their pad'{e} approximants, in the sense of uniform convergence on compacta. In this paper we examine a more particular space, $A^{\mathrm{\infty }}(\mathrm{\Omega })$, and prove that we can obtain similar approximation results with functions smooth on the boundary.