analytic function ( pole)

sbashrawi

1. The problem statement, all variables and given/known data

Let r>1, let f be analytic in the disc (0,r)\{1}, and suppose that f has apole at 1.

Let sum(a(k) *z(k)) be the power series expantion of f in the disc (0,r). Prove that there is a positive integer N so that a(k) not equal to zero for k>= N, and that

lim (a(N+j+i)/a(N+1))=1


2. Relevant equations



3. The attempt at a solution

sbashrawi

no body replied on this problem

is it so hard?