How do I evaluate ?
I've tried using substitution and splitting it into partial fractions, but they end up taking many sides of paper and leading to dead ends!
I'm afraid I haven't studied residues yet and, upon checking my notes, there doesn't appear to be anything on them at all!residues at z=0 and z=i/2.
I have and i need to calculate the residues at and . I found this method on wikipedia and i'll try and follow through that (http://en.wikipedia.org/wiki/Residue_(complex_analysis).
Parameterisation of the unit circle where .
This means I have to calculate
However, for
This means that the following terms are going to have some value:
hmm, evaluating this will give me a ..... =S