An asymptotic study of a recursion occurring in the analysis of an algorithm on broadcast communication

摘要

Shiau and Yang (1996) proved that a certain quantity T_n occurring in the analysis of an algorithm on broadcast communication satisfies 4≤Tn/log n)≤5. We give an explicit expression for T_n involving Bernoulli numbers and a precise asymptotic formula showing in particular that T_n/(log n) →π~2/(3 log2) =4.74627644...