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Dec4-11, 07:13 AM
P: 1,666
Quote Quote by matematikuvol View Post
Thanks mate. Sorry again. Is there some easy way to see that that integral will go to zero? When you see

Ok, that one "looks" like you're just going around the origin but really you mean the half-disc contour in either half-plane. Around the origin, the integral is 2pi i. Otherwise if it's around the discs. You could be more specific like:

[tex]\mathop\oint\limits_{|z|=1} \frac{e^{ikz}}{z}dz[/tex]

that's really clear or in the other case:

[tex]\mathop\oint\limits_{D} \frac{e^{ikz}}{z}dz[/tex]

then clearly specify in the text what D is. In regards to you question about the integral over the upper half-disc around the semi-circle, well, you just need to plug it all in and analyze it to see what happens as R goes to infinity.