Coincidence of Two Classes of Universal Laurent Series

There exist functions, called U.L.S. (Universal Laurent Series), holomorphic on finitely connected domains Ω in C, whose Laurent-type partial sums approximate everything we can hope for, on compact subsets outside Ω ∪ {a ₁,…,a}, for certain prescribed points a ₁,…,a _k. In this paper we prove that, under additional assumptions, for every U.L.S. there exists a subsequence of its Laurent-type partial sums, which converges to the function itself in the whole of Ω and which approximates everything we can hope for outside Ω ∪ {a ₁,…,a, _k}.

Keywords:

• Generic Property
• Universal Laurent Series