Zeros of Padé approximants for some classes of functions

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Institute of Mathematics, Bulgarian Academy of Sciences, BG-1090 Sofia, Bulgaria

In the present paper, we deal with functions

f (z) := \sum_{n = 0}^{\infty} a_{n} z^{n}

whose coefficients satisfy a special smoothness condition. Theorems concerning the asymptotic behaviour as

\to \infty, m - f i x e d, o f t h e ∥ a ∥ l i z e d \in a n a p \propto r i a t e w a y P a d é \approx i m a n t s

π_{n,m}!$! are provided. As a consequence, results concerning the limiting distribution of the zeros are deduced.

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