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I'm trying to find Fourier series for the following function:

[tex]f(x) = \begin{cases}1, & \mbox{if x $\in (-\frac{\pi}{2}+2\pi n,\frac{\pi}{2}+2\pi n)$ } \\

-1, & \mbox{if x $\in [\frac{\pi}{2}+2\pi n,\frac{3\pi}{2} + 2\pi n]$} \end{cases}[/tex]

This is how I calculated a_n and b_n:

[Please See 2.pdf and 3.pdf]

So I got the following series: [tex] \sum_{n=1}^{\infty} \cos{nx}\frac{4(-1)^{n+1}}{\pi(2n-1)}[/tex]

But when I checked if it converges to f(x) at point \pi I get that it diverges, however all requirements of Fourier theorem are met.

What am I doing wrong?

[tex]f(x) = \begin{cases}1, & \mbox{if x $\in (-\frac{\pi}{2}+2\pi n,\frac{\pi}{2}+2\pi n)$ } \\

-1, & \mbox{if x $\in [\frac{\pi}{2}+2\pi n,\frac{3\pi}{2} + 2\pi n]$} \end{cases}[/tex]

This is how I calculated a_n and b_n:

[Please See 2.pdf and 3.pdf]

So I got the following series: [tex] \sum_{n=1}^{\infty} \cos{nx}\frac{4(-1)^{n+1}}{\pi(2n-1)}[/tex]

But when I checked if it converges to f(x) at point \pi I get that it diverges, however all requirements of Fourier theorem are met.

What am I doing wrong?