freechus9
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Hello, I am working on a problem and I have to solve a nasty integral. The problem is that I am not sure if the method I am using is correct.
The integral I need to solve is:
\int^{\infty}_{-\infty}\frac{e^{ikx}dk}{\sqrt{k^2 + a} - (b\pm i\lambda)}
At this point, I have tried multiplying the top and bottom by \sqrt{k^2 + a} + (b\pm i\lambda) and continuing forth by splitting into partial fractions and using the Cauchy residue theorem, but I am not sure if this is a valid way to solve this.
If anyone has any insight I would be more than indebted! Thank you so much!
The integral I need to solve is:
\int^{\infty}_{-\infty}\frac{e^{ikx}dk}{\sqrt{k^2 + a} - (b\pm i\lambda)}
At this point, I have tried multiplying the top and bottom by \sqrt{k^2 + a} + (b\pm i\lambda) and continuing forth by splitting into partial fractions and using the Cauchy residue theorem, but I am not sure if this is a valid way to solve this.
If anyone has any insight I would be more than indebted! Thank you so much!