define analyticity of a function
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A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function"
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A function is said to be analytic in the region T of complex plane x if, f(x) has derivative at each and every point of x and f(x) has unique values that are it follows one to one function. ' This example explains the analytic function on the complex plane. Let f:C\rightarrow C be an analytic function.
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