 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"0 converges to the function in some neighborhood for every "x"0 in its domain.Formally, a function formula_1 is "real analytic" on an open set formula_2 in the real line if for any formula_3 one can write

in which the coefficients formula_5 are real numbers and the series is convergent to formula_6 for formula_7 in a neighborhood of formula_8.