The has singularities at z=0 and z=4 so you will be able to find two series. One for 0<|z|<4 and for |z|>4. Where did you get your values?
Can someone show me how to find the Laurent series of 1/z(z-4) expanded in terms of z-1? I can figure out the expansion for the domain 1 < abs(z) < 3, but I'm having trouble with the other two domains (i.e. 0 < abs(z) < 1 and abs(z) > 3.
Thanks for your help.
The objective is to get the expressions in terms of a geometric series of the form where in the domain of interest. First write the function as . For the domain start by adding and subtracting one in the denominator:
Now in the case of , you need to have geometric terms which are less than one for . I'll do the first term:
Do the second one to get:
Thus: