Editing Radius of convergence (section)

{{short description|Domain of convergence of power series}}
In [[mathematics]], the '''radius of convergence''' of a [[power series]] is the radius of the largest [[Disk (mathematics)|disk]] at the [[Power series|center of the series]] in which the series [[Convergent series|converges]].  It is either a non-negative real number or <math>\infty</math>.  When it is positive, the power series [[absolute convergence|converges absolutely]] and [[compact convergence|uniformly on compact sets]] inside the open disk of radius equal to the radius of convergence, and it is the [[Taylor series]] of the [[analytic function]] to which it converges. In case of multiple singularities of a function (singularities are those values of the argument for which the function is not defined), the radius of convergence is the shortest or minimum of all the respective distances (which are all non-negative numbers) calculated from the center of the disk of convergence to the respective singularities of the function.