Zeros of Padé approximants for some classes of functions
Volume 37 / 1996
Banach Center Publications 37 (1996), 243-250
DOI: 10.4064/-37-1-243-250
Abstract
In the present paper, we deal with functions $f(z) := ∑_{n=0}^{∞} a_{n} z^{n}$ whose coefficients satisfy a special smoothness condition. Theorems concerning the asymptotic behaviour as $ → ∞, m - fixed, of the normalized in an appropriate way Padé approximants $π_{n,m}$ are provided. As a consequence, results concerning the limiting distribution of the zeros are deduced.
