Radius of convergence of power series

Given a meromorphic function on $\mathbb{C}$, is the radius of convergence in a regular point exactly the distance to the closest pole?

As Robert Israel points out in his answer, that this is of course an upper bound by the Cauchy-Hadamard principle.

Theo Buehler in the comments gives a refernce for the non obvious direction: Remmert, Theory of complex functions, Chapter 7, §3, p.210ff (p. 164ff of my old German edition). Look for Cauchy-Taylor.

Yes, it is (that should be "pole", not "pol"). If $r$ is the distance from $z_0$ to the closest pole, the function is analytic in $\{z: |z - z_0| < r\}$, so the radius of convergence is at least $r$, but it can't be more than $r$ because $|f(z)| \to \infty$ as $z$ approaches that pole.

Give an example of a noncyclic Abelian group all of whose proper subgroups are cyclic.

How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?

Any good decomposition theorems for total orders?

Convergence a.e. and of norms implies that in $L^1$ norm

How to find all subgroups of $(\mathbb{Q},+)$

The closed graph theorem in topology

Approximating $\pi$ with least digits

Solving two-dimensional recurrence relation $a_{i,\ j}\ =\ a_{i,\ j-1}\ +\ a_{i-1,\ j-1}$

A polynomial that is zero on an open set

Proof of existence of a limit for the sequence recursively-defined with $a_1=1$, $a_2=1$ and $a_n=\frac{1}{a_{n-1}}+\frac{1}{a_{n-2}}$ for $n\ge2$

Why can 2 uncorrelated random variables be dependent?

How prove this inequality $\sum\limits_{cyc}\frac{x+y}{\sqrt{x^2+xy+y^2+yz}}\ge 2+\sqrt{\frac{xy+yz+xz}{x^2+y^2+z^2}}$