Question

Find the Laurent's expansion of e to the power of 2z/(z-1)to the power 3 about the singularity z=1

Answer 1

Answer:

The coefficients of this Laurent expansion are computed the same way as Taylor's. The question is how is that possible? If function is not holomoprhic at z=0, then it's not true that it is holomophic at |z|<R and Taylor's coefficients can not be used. Please someone explain.