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## Homework Statement

The function g(x) is defined as follows:

[tex] g(x) = \left\{ \begin{array}{rcl}

{-\pi e^x} & \mbox{for}

& -\pi < x < 0 \\

{\pi e^{ -x}} & \mbox{for} & 0 < x < \pi

\end{array}\right. [/tex]

And the Fourier series for g(x) is as follows:

[tex]

\sum_{n=0}^\infty \frac{2n}{n^2+1}(1 - (-1)^n e^{-\pi})\sin{nx}

[/tex]

What is the sum of this series given [tex] x = \frac{\pi}{2} [/tex] and [tex]x = \frac{3\pi}{2} [/tex]?

## The Attempt at a Solution

We've tried googeling, adressing the textbook on the subject (Kreyzig's Advanced Engineering Mathematics), but have yet to find a solution to this problem. Any help would be greatly appreciated! :)