In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at a point if, in some neighborhood of that point, it is equal to a power series centered there. The analytic function is therefore locally determined by coefficients of the series, or equivalently by derivatives of the function evaluated at the center of the series expansion. In other words, an analytic function is a function that is locally represented by a convergent Taylor series.