Infinitely differentiable functions are also called as smooth functions in mathematics. Any analytic function of a real argument is smooth, but the converse is not true. An analytic function is a function given by a convergent power series. A function is analytic only if its Taylor series about x0 converges to the function for every x0 in its domain. Such as all polynomials, exponential function, trigonometric functions, logarithm, and the power functions.