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
x0 converges to the function in some
neighborhood for every
x0 in its domain.