Segments of exponential series and regularly varying sequences

Abstract

The task of this paper is to investigate asymptotic behavior of segments of exponential series defined as Tλ(x):= ∑n<λx Cn/n! xn, λ ∈ R +, x → ∞, where (cn)n ∈ N belongs to the set of regularly varying sequences in Karamata sense of arbitrary index. Precise results are obtained.