- 6

- 0

## 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.)

- Thread starter fivestar
- Start date

- 6

- 0

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.)

morphism

Science Advisor

Homework Helper

- 2,013

- 4

- 6

- 0

Thanks again.

HallsofIvy

Science Advisor

Homework Helper

- 41,738

- 899

" 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 [itex]f(x)= e^{-\FRAC{1}{x^2}}[/itex] if x is not 0. f(0)= 0 is infinitely differentiable but **not** analytic.

Why would that be presumed? The question was whether or not the fact tha a function is

Last edited by a moderator:

morphism

Science Advisor

Homework Helper

- 2,013

- 4

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

mathwonk

Science Advisor

Homework Helper

- 10,744

- 920

simply out, for complex functions, the answer is yes.