The Asymptotic Behavior of a Class of Entire Functions

Abstract

z = zp ; argzp argz -2p7r/s; p pm; and lim w(zp,n) =0. If k m=1 ZI 1->oo is even the same conclusion results except that the limits uponl the first summation are c/2 and (k 2) /2 when 27r/s < arg z < 0, and are -(c -2)/2 and k/2 when 0 < argz < 27r/s. The asymptotic behavior of the same function was considered by Van Engen 1 in his dissertation, but the method employed here is sufficiently general that it appears to offer an approach to the study of a large class of entire functions related to (1).