1. ## Integral over angles

How to calculate:

$I = \int_0^{4\pi} d\Omega \frac{exp(i \hat{n}\vec{a})}{1-(\hat{n}\vec{b})^2}$,

where a and b are fixed vector, and n is a unit vector pointing in the Omega direction.

2. Originally Posted by Heirot
How to calculate:

$I = \int_0^{4\pi} d\Omega \frac{exp(i \hat{n}\vec{a})}{1-(\hat{n}\vec{b})^2}$,

where a and b are fixed vector, and n is a unit vector pointing in the Omega direction.
In spherical coordinates $d \Omega = sin( \theta )d \theta d \phi$. But your integrand contains neither variable(?) So thus your integrand is constant with respect to both angles and can be taken outside of the integral.

-Dan

3. Actually, $\hat{n}=(sin(\theta) cos(\phi), sin(\theta) sin(\phi), cos(\theta))$.