Zeros of Padé Approximants for Entire Functions with Smooth Maclaurin Coefficients Original Research Article

For entire functions ƒ(z) = Σ∞j=0ajzj whose coefficients satisfy the smoothness condition aj+1aj−1/a2j → η as j → ∞ we investigate the asymptotic behavior as n → ∞ of the normalized partial sums sn(zan/an+1 and the normalized Padé numerators Pn,m(zan/an+1), m fixed. As a consequence we deduce results on the limiting behavior of the zeros of these polynomials.