Can I have a help for a Laurent Expansion for the following? I need it on summation notation using the general formula below.

I want it done on this way

If it cannot be carried out that way, one can make use of the general form of a laurent series. Please provide a contextual explanation on the solution clearly as well as necessary information, specifically on the mathematical part one. Here are the problems

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f(Z) = A,(Z - Z.) where 1 f(E) dž An 2ni (n = 0, +1, +2, ...). | f(Z) = A,(Z - Z.) where 1 f(E) dž An 2ni (n = 0, +1, +2, ...). |