<P> In mathematics , an analytic function is a function that is locally given by a convergent power series . There exist both real analytic functions and complex analytic functions , categories that are similar in some ways , but different in others . Functions of each type are infinitely differentiable , but complex analytic functions exhibit properties that do not hold generally for real analytic functions . A function is analytic if and only if its Taylor series about x converges to the function in some neighborhood for every x in its domain . </P>
<P> In mathematics , an analytic function is a function that is locally given by a convergent power series . There exist both real analytic functions and complex analytic functions , categories that are similar in some ways , but different in others . Functions of each type are infinitely differentiable , but complex analytic functions exhibit properties that do not hold generally for real analytic functions . A function is analytic if and only if its Taylor series about x converges to the function in some neighborhood for every x in its domain . </P>
when is a function said to be analytic
when is a function said to be analytic
if and only if its Taylor series about x converges to the function in some neighborhood for every x in its domain
if and only if its Taylor series about x converges to the function in some neighborhood for every x in its domain