Condition: $a$ is a real number but not integer.
(1) $f(x)=e^{-iax},(-\pi<x<= \pi)$. expand $f(x)$ onto the real axis with period $T=2\pi$. Find the complex Fourier series of $f(x)$.
(2) prove that $$\sum_{n=-\infty}^\infty \frac{1}{(n+a)^2} = \frac{\pi^2}{(sin(a\pi))^2}$$
My solution for question 1 is as below. Is it right? How can I do the 2nd question?
Solution for 1: $c_n= \frac{1}{2\pi} \int_{-\pi}^{\pi} e^{-iax}e^{-inx} dx = \frac{sin((a+n)\pi)}{i\pi(a+n)}$
so $ f(x)= \sum_{-\infty}^{\infty} \frac{sin((a+n)\pi)}{i\pi(a+n)}* e^{inx} $
Really appreciate your help.