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Math Help - Partial fraction decomposition of tangent function

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    Complex Analysis: Partial fraction decomposition of tangent function

    Hey, howdy!

    My book asked me to show, using the relation cot(z/2) -tan(z/2) = 2 cot(z), that pi*tan(pi*z) = sum[(8*z)/((2*n+1)^2 - 4*z^2)]

    But I was only able to get that pi*tan(pi*z) = sum[(2*z)/(z^2 - n^2) - (8*z)/(4*z^2 - n^2)].

    Oh and I used, of course, that pi*cot(pi*z) = 1/z + sum[(2*z)/(z^2-n^2)].

    How do I proceed from here?

    Thanks!
    Last edited by joshquick; December 7th 2010 at 03:22 PM.
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