In Shannon's 1948 paper "A Mathematical Theory of Communication", early on he derives the equation

N(t) = N(t-t1) + N(t-t2) + … + N(t-tn)

He then says "according to a well-known result in finite differences,N(t)is then asymptotic for largetto(X0)^twhere(X0)^tis the largest real solution of the equation

X^(-t1) + X^(-t2)+…+X^(-tn) = 1"

He does not cite a reference.

Intuitively,it seems to be true.but someone can help me in details? or tell me the reference at least. thx~

here is the paper: