# Antiderivitives of complex functions

## Main Question or Discussion Point

My question is dose the existance of an antiderivitive in a domain imply that the function is anaylitic in that domain? (when f(x) is continous on that domain.)

## Answers and Replies

morphism
Homework Helper
Presumably this antiderivative is analytic on the domain, and hence so is its derivative, which is f.

Thanks for the reply. Let me make sure i have this right. A function is only analytic if its antiderivitive is analytic? That means that just the existance of an antiderivitive alone dose not show that the function is analytic?

Thanks again.

HallsofIvy
Homework Helper
" Presumably this antiderivative is analytic on the domain, and hence so is its derivative, which is f."

Why would that be presumed? The question was whether or not the fact tha a function is once differentiable is enough to conclude that is is analytic on an interval. The function $f(x)= e^{-\FRAC{1}{x^2}}$ if x is not 0. f(0)= 0 is infinitely differentiable but not analytic.

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morphism
Homework Helper
Why would that be presumed?
Because I was under the impression that this question was complex analytic in flavor, i.e. that we're talking about complex derivatives.

mathwonk