# Questions tagged [entire-functions]

This tag is for questions relating to the questions on entire functions. The polynomials which form a special and important class of entire functions, can be characterized as those entire function which have at most a pole as a singularity at infinity.

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### Suppose $f_1,f_2$ entire functions. Produce entire $h,g_1,g_2$ such that $f_1=hg_1$ and $f_2=hg_2$ with $g_1,g_2$ no common zeros.

Suppose $f_1,f_2$ entire functions. Produce entire $h,g_1,g_2$ such that $f_1=hg_1$ and $f_2=hg_2$ with $g_1,g_2$ no common zeros. I know I have to use Weierstrass factorization theorem somehow but I’...
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### Maximum value of an entire function in a closed set.

Consider the entire function $f(z)=z(z-i)$. Put $$S=\bigg\{\frac{1}{|f(z)|}\ |\ |z|\geq 2\bigg\}.$$ At what value(s) of $z$ is the maximum of the set $S$ attained? My Idea: As $f(z)$ is an entire ...
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### Proving that the entire function which satisfies a given property is unique

Let $\phi : \mathbb{C} \to \mathbb{C}$ be an entire function satisfying the following three properties: $|\phi'(z)| \leq |\phi(z)|$ for all $z \in \mathbb{C}$ $\phi(0) = 2$ $\phi(1) = 1$ The problem ...
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