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1. Homework Statement
Hi, I need to calculate the following integral:
[itex]\int_{\infty}^{+\infty}dx \frac{(\pi+\sqrt{x^2+m^2})^2(1+\cos x)}{(x^2\pi^2)^2\sqrt{x^2+m^2}}[/itex]
3. The Attempt at a Solution
I tried complexifying it:
[itex]\oint dz \frac{(\pi+\sqrt{z^2+m^2})^2(1+e^{iz})}{(z^2\pi^2)^2\sqrt{z^2+m^2}}[/itex]
And having this over the following contour (sorry for the quality of the image):
https://www.dropbox.com/s/t7ioou1kjs3y7ej/paint.jpg?dl=0
The red dots are the poles at: [itex]\pm\pi[/itex] and [itex]\pm im[/itex].
But is it a valid contour in this case, or should I pay extra attention to the branch cuts of the sqrt in the denominator? If so, how do I choose the contour properly?
Hi, I need to calculate the following integral:
[itex]\int_{\infty}^{+\infty}dx \frac{(\pi+\sqrt{x^2+m^2})^2(1+\cos x)}{(x^2\pi^2)^2\sqrt{x^2+m^2}}[/itex]
3. The Attempt at a Solution
I tried complexifying it:
[itex]\oint dz \frac{(\pi+\sqrt{z^2+m^2})^2(1+e^{iz})}{(z^2\pi^2)^2\sqrt{z^2+m^2}}[/itex]
And having this over the following contour (sorry for the quality of the image):
https://www.dropbox.com/s/t7ioou1kjs3y7ej/paint.jpg?dl=0
The red dots are the poles at: [itex]\pm\pi[/itex] and [itex]\pm im[/itex].
But is it a valid contour in this case, or should I pay extra attention to the branch cuts of the sqrt in the denominator? If so, how do I choose the contour properly?
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