Zeros of Sections of Divergent Power Series

Abstract

The zero distribution of appropriately normalized partial sums of power series with zero radius of convergence is studied in general as well as under certain conditions on the coefficients. The special polynomial sequencesn(z)≔1+z+2!z2+···+n!znis studied in detail; explicit bounds for the moduli of the roots ofsn(ze/n)=a(a≠1) are given, and it is shown that the roots have uniform angular distribution.