A note on the limiting distribution of the zeros of Padé approximants for some classes of functions

In the present paper, we deal with functions f(z) := ∑∞n=0 anzn whose coefficients satisfy a special smoothness condition. Theorems concerning the asymptotic behaviour as n → ∞, m-fixed, of the normalized in an appropriate way Padé approximants πn,m are provided. As a consequence, results concerning the limiting distribution of the zeros are deduced.