Suppose that is a power series of the form Then for any r, 0 < r < 1, has zeros in .
We apply Jensen's theorem (Theorem 3.61 of [17]). If are the zeros in |z| < R, where r < R < 1, then we find that since . Therefore, if m is the number of zeros in |z| < r, we have Since we obtain We now choose , and this yields the bound . (Better bounds can be obtained by selecting R more carefully or estimating the integral of in Jensen's theorem better.)