radius of convergence

radius of convergence (plural radii of convergence)

1. for a power series ${\displaystyle \sum _{n=0}^{\infty }c_{n}(z-a)^{n}}$, the unique number ${\displaystyle R=[0,\infty ]}$ such that the sum is convergent for ${\displaystyle |z-a|<R}$, and divergent for ${\displaystyle |z-a|>R}$