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jackmell
#17
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

[tex]\oint\frac{e^{ikz}}{z}[/tex]?
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.