- Thread starter
- #1

- Jan 31, 2012

- 253

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?

- Thread starter Random Variable
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- Thread starter
- #1

- Jan 31, 2012

- 253

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?

- Jan 17, 2013

- 1,667

Yeah, I must confess , that wasn't easy to see at the first glance, at least for me. I was trying just like you to find an upper bound

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?

- Jan 17, 2013

- 1,667

Well, I guess I am going senile at the age of 23

- Thread starter
- #4

- Jan 31, 2012

- 253

And then mrf had to rub it in by mentioning that $e^{iz}$ of course has an elementary antiderivative that is valid everywhere since $e^{iz}$ is an entire function.

I could have at least recognized that there was no justification for bringing the limit inside of the integral due to the fact that parametrization of the integral brings an $R$ out front.

I could have at least recognized that there was no justification for bringing the limit inside of the integral due to the fact that parametrization of the integral brings an $R$ out front.

Last edited:

- Jan 17, 2013

- 1,667

I recognized that the function has an anti-derivative but that was a little bit late .

- Feb 15, 2012

- 1,967

I went senile already. Wasn't working for me.

- Feb 13, 2012

- 1,704

If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?

... sometime just take it easy! ...

Kind regards

$\chi$ $\sigma$

- Mar 22, 2013

- 573

- Admin
- #9

Yes you are, since you are now 14.I am already senile at 13...

- Mar 22, 2013

- 573

- Admin
- #11

I guess if Jack Benny could be 39 forever, then you can be 13 for a few years.

- Admin
- #12

- Jan 26, 2012

- 4,093

- Jan 17, 2013

- 1,667

True. Working with some complicated stuff , you always miss the trivial. Sometimes it needs no more than thinking simple to find the solution.If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

... sometime just take it easy! ...

Kind regards

$\chi$ $\sigma$

- Jan 29, 2012

- 1,151

That's why I drink so much- so I can claim I'm not senile.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?

- Jun 26, 2012

- 45

Is there a converse of Morera's theorem?