I am trying to find the Fourier Transform of the periodic function
$$ f (\theta) = \sum_{n=- \infty}^{\infty} a_n \space \exp(i n \theta)$$.
Using the formula, $$ f(k) = \int_{- \infty}^{\infty} d \theta \space \exp(-ik \theta ) f(\theta)$$
I get the following infinite sum $ 2 \pi a_n \sum_{n=- \infty}^{\infty} \space \delta (k - n)$
Where do I go from here?