Are any complex-valued polynomials infinitely differentiable?
Prove that any polynomial is infinitely differentiable for my calculus exam in master. the book i am studying mentions complex-valued functions. so maybe polynomial has to be complex-valued. and its written end of the chapter : The functionf: (a, b) -> C is said to be of class C^k, or k-times continuously differentiable, if each of the derivatives f, f',…,f^k is a continuous function on (a, b). The function is said to be a class C^∞ , or infinitely differentiable, if f is continuous on (a, b) for every integer k >= 0
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