ANALYTIC AND NON- ANALYTIC FUNCTION AND THEIR CONDITIONS, PROPERTIES AND CHARACTERIZATION

In Mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic function & complex analytic functions. We can also say that A function is a Analytic iff it's Taylor series about xo in its domain. Sometimes there exist smooth real functions that are not Analytic known as Non- Analytic smooth function.In fact there are many such functions. Function is Analytic & Non- Analytic at some conditions which are mentioned. Properties and Characterization of Analytic and Non- Analytic functions are very vast and these are very helpful to solve our problems in many ways. Some of these properties are same as in Analytic function with several variables.