How to solve this integral (complex variables - green's function)

51 Views Asked by At

I am trying to resolve the following EDP $$(\nabla^2+m^2)f(x,y,z)=g(x,y,z),$$ where $m$ is a constant (very small).

For that, I'm using Green's Method of Functions. In developing the solution I obtained the following integral to solve

$$I=\int_{-\infty}^{+\infty} dk \frac{k \sin(k a)}{k^2-m^2},$$ where $a$ is a positive constant.

Please help me, I am getting a result proportional to the cosine, but I need that in the limit of a tending to infinity my solution go to zero!