# Properties of Entire Functions

a). Suppose an entire function f is bounded by M along $\vert z \vert = R$. Show that the coefficients $C_k$ in its power series expansion about $0$ satisfy $\vert C_k \vert \leq \frac{M}{R^k}$.

I know that an entire function is infinitely differentiable and can be represented as a power series $C_k = \sum_{k=0}^{\infty} \frac{f^{k}(0)}{k!}z^k$. However, I am not too sure what is meant by $M$.

Source: I am using the Complex Analysis, Third Edition textbook by Bak and Newman.

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–  1015 Mar 19 '13 at 5:13
No source, no sign of effort by OP, no indication of what OP knows, where OP gets stuck ... voting to close. –  Gerry Myerson Mar 19 '13 at 5:13
It would probably be best to ask just one of the two questions here. You can ask the second one separately. –  Antonio Vargas Mar 19 '13 at 13:48
Thank you for the advice, I just edited the question. –  Jamil_V Mar 19 '13 at 13:50