# Math Help - Question on power series coefficient of bounded function

1. ## Question on power series coefficient of bounded function

I have a function f holomorphic on D(0;R).

s, r such that (r < s < R)

M(r) = sup { |f(z)| : z = r } (r < R)
M(s) = sup { |f(z)| : z = s } (s < R)

I was asked to show that M(r) <= M(s) and I have used the Maximum Modulus and the Identity theorems to accomplish that.

The next part of question asks to show that M(r) r^(-n) >= M(s) s^(-n) when f is a polynomial of degree n 0 < r < s < R.

I know that f(z) = Sum ( Cn (z - a)^n ) from 0 to inf

and

M(r) r^(-n) >= | An |
M(s) r^(-n) >= | Bn |

Could someone push me in the right direction?
Thanks!

2. ## Re: Question on power series coefficient of bounded function

Use maximum modulus principle with $Q(z):=z^nP(z^{-1})$.