Here is my problem:(adsbygoogle = window.adsbygoogle || []).push({});

I need to integrate:

[tex] (\frac{sin \alpha z}{\alpha z})^2\frac{\pi}{sin\pi z}[/tex]

around a circle of large radii and prove:

[tex]\sum_{m=1}^\infty(-1)^{n-1}

(\frac{sin m\alpha}{m\alpha})^2

=\frac{1}{2}[/tex]

I'm kind stumped.

I've been looking at books for a while now and the only useful things i've discovered are:

[tex]\frac{\pi}{sin \pi z}=\Gamma(z)\Gamma(1-z)[/tex]

and also

[tex] \frac{sin z}{z}=\sum_{n=0}^\infty C_n z^{2n-1}[/tex]

Can anyone help me out?

Thanks!

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# Hard problem

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