Let $f_1$ and $f_2$ be entire functions of growth order $a$ and $b$ such that $a$ and $b$ are different. I managed to show that the growth order of the product of the two functions is less or equal than the maximum of $a$ and $b$. However now I am required to prove that the growth order is 'equal' to the the maximum of $a$ and $b$. I can't find a way to show the equality...Could anyone help me?
2026-03-27 13:25:55.1774617955
Computing the order of the product of two entire functions
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This requires an estimate of the entire function of smaller order from below, which is not trivial. Look in B. Levin, Distribution of zeros of entire functions. American Mathematical Society, Providence, R.I., 1980, Chap. I, $\S$ 9, Theorem 12 a).