Erdos, F eller, and Pollard [2] pro ved that if the greatest common divi or of the k's with c,,>O is 1, then , Other theorems of the same type as theorem 1 were proved by T . Kaluza [4] . Assuming (1) , he showed for instance, that j (2) > 0, j (n l )j (n + 1) > p(n ) (n = 2,3, . .. ) imply that the c's are positive. Furthermore, he proved that j (I ),j(2), ... is a moment equence if, and only ...

In this text we study, for positive random variables, the relation between the behaviour of the Laplace transform near infinity and the distribution near zero. A result of De Bruijn shows that E(e−λX) ∼ exp(rλ) for λ → ∞ and P (X ≤ ε) ∼ exp(s/ε) for ε ↓ 0 are in some sense equivalent (for 1/α = 1/β + 1) and gives a relation between the constants r and s. We illustrate how this result can be use...

This paper provides the asymptotic analysis of the loss probability in the GI/M/1/n queueing system as n increases to infinity. The approach of this paper is alternative to that of the recent papers of Choi and Kim [8] and Choi et al [9] and based on application of modern Tauberian theorems with remainder. This enables us to simplify the proofs of the results on asymptotic behavior of the loss ...