Laurent series of entire function

Question

A complex function is analytic in Domain $D$ if and and only if it's Laurent series ( in the neighborhood of any complex number in $D$ ) has no principal part. Am I right ?

Answer 1

If a function $f : D \rightarrow \mathbb{C}$ is holomorphic, then what can you say about $\oint_{\gamma} (z-z_0)^n \, f(z) \, dz$ for $n \geq 0$? (where $z_0$ is a point in $D$ and $\gamma$ is a simple closed curve enclosing $z_0$ lying in $D$)

If the Laurent series of $f$ about a point $z_0$ has no principal part, then it is just a power series about $z_0$ which converges in its disk of convergence. Does it define a holomorphic function?