On the summability of functions analytic in star-shaped domains

Let $f(z)$ be a function which is analytic over the whole plane except for an arbitrary interval $\Delta$, $0\overline\in\Delta n$. Suppose that $f(z)$ has a power series expansion about the origin. We prove that a matrix exists which sums the power series to $f(z)$ over the whole plane except for $\Delta$.