Question

Do you agree with the following statement? “An analytic function is miraculous because its values on a simple closed contour determine its values at every point on the region inside it.” Discuss why or why not (your answer does not have to be lengthy, but try to be precise about your reasons).

Answer 1

No, “An analytic function is not miraculous because its values on a simple closed contour determine its values at every point on the region inside it.”

As analytic functions are meant to be continuous and hence, it yields values at every point within the region of simply closed contour.

But if the contour is not simply closed still we can play with analytic function and get the result of integral. In this case, it is miraculous.

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Thank you!