Cotangent and Cosecant's Laurent Expansion
Formula
$$ \cot z = {{1} \over {z}} - {{z} \over {3}} - {{z^{3}} \over {45}} - {{2 z^{5}} \over {945}} - \cdots \\ \csc z = {{1} \over {z}} + {{z} \over {6}} + {{7 z^{3}} \over {360}} + {{31 z^{5}} \over {15120}} + \cdots $$
Description
In complex analysis, to use the sum of series formula, it is necessary to be able to find the residue of functions multiplied by cotangent and cosecant. Of course, there are more elegant series forms that can be used for terms of higher order, but this is usually sufficient. It would be advisable to memorize the coefficients up to at least the third term for exam preparation.