Analyticity
= Analyticity
Analyticity at a point means that a <function> agrees in a neighbourhood of that point with a convergent <power series>. This is stronger than merely having <derivatives> of every order: the <Taylor series> of a <smooth function> can fail to recover its values. For a real variable this property defines a <real analytic function>. For a complex variable it is equivalent to being a <holomorphic function> on a neighbourhood of the point.