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- Jun 20, 2014

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Let $F$ be an entire function for which there exists $t > 0$ such that $\lvert F(z)\rvert = O(\exp(\lvert z\rvert^t))$ as $\lvert z\rvert \to \infty$. Show that there is a constant $M > 0$ such that for all $n$ sufficiently large, $$\lvert F^{(n)}(0)\rvert \le Mn!\left(\frac{et}{n}\right)^{n/t}$$

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