ZEROS OF SECTIONS OF DIVERGENT POWER-SERIES

The zero distribution of appropriately normalized partial sums of powe r series with zero radius of convergence is studied in general as well as under certain conditions on the coefficients. The special polynomi al sequence s(n)(z) := 1 + z + 2!z(2) + ... +n!z(n) is studied in deta il; explicit bounds for the moduli of the roots of s(n)(ze/n) = a (a n ot equal 1) are given, and it is shown that the roots have uniform ang ular distribution. (C) 1996 Academic Press, Inc.