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

We deal with functions f(z) ≔ Σ∞n = 0anzn whose coefficients satisfy Lubinsky′s smoothness condition, namely, aj + 1· aj − 1/a2j → η as j → ∞, η ≠ ∞. In the present paper, theorems concerning the asymptotic behaviour of the normalized (in an appropriate way) Padé error functions (f − πn,m) as n → ∞, m-fixed, are provided. As a consequence, results concerning the number of the zeros and of their limiting distribution are deduced.