Let $f$ be an entire function on the complex plane.
Is the radius of convergence of $f$ around any point $z_0$ infinite? If so, why?
Thank you.
2026-04-05 18:49:05.1775414945
Radius of convergence of entire function
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A function $f: \mathbb{C} \to \mathbb{C}$ is said to be entire if it is holomorfic in the all complex plane, but using the Cauchy's Integral Formula, we have that a holomorfic function in a region is also analytic in this same region region. Therefore, therefore an entire function $f$ is analytic in the all complex plane, but we also have that the radius of convergente of a series centered in a point $z_0$ is the distance between $z_0$ and the nearest singularity of the series, in that case, it is going to be infinite.