Fourier Series of $f(x)=e^x$ on $[0,\pi)$ as a function of period $\pi$

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Can you tell me what you get? I've tried computing it, I've got some result but I don't think it's right since I need to use it for something else and it doesn't work at all... What exactly I'm trying to do is to find a infinite sum corresponding to $coth(\pi/2)$, do you see anything?

Thank you!

what I get:

$\exp(x) \sim \dfrac{2\sinh(\pi/2)}{\pi}+ \sum \left[\tfrac{4(-1)^n \sinh(\pi/2)}{8n^2+\pi}\cos(2nx) - \tfrac{8n(-1)^n \sinh(\pi/2)}{8n^2+\pi}\sin(2nx)\right]$

That seems totally wrong...