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Determine all entire functions $f(z)$ such that $0$ is a removable singularity of $f\big(\frac{1}{z}\big)$.

I have no idea how to start with.

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closed as off-topic by Saad, Chinnapparaj R, Brahadeesh, rtybase, ancientmathematician Dec 1 '18 at 15:56

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By Reimann Theorem for removable singularity, If $ f$ has a removable singularity at $z_0$ iff it is bounded and holomorphic in a neighbourhood

SO as $g(z)=f(1/z)$ has removable singularity at 0 so at infinity $f(z)$ is bounded so

By Liouvillies theorem

f is constant

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