Disk of convergence ($\{z\in \mathbb{C}:|z-c|<R\}$)

For a power series centred at $c$ with radius of convergence $R$, its disk of convergence is the open disk $|z-c|<R$, on which the series has absolute convergence. Boundary points may or may not belong to the larger domain of convergence. When $R=0$ this open disk is empty, although the power series still converges at its centre; when $R=\infty$ it is the whole complex plane.