Question

Determine the following Laurent Series:
\[\frac{1}{z-i}+\frac{1}{z+1} \] on
\[ [Z \in C, 0<\left| Z +1 \right|<\sqrt{2}]\]

Answer 1

Use the geometric series..

Answer 2

\[\frac{1}{z+1-(1+i)}\]

Answer 3

?? i was thinking something like this

Answer 4

\[-\frac{1}{1-i} \frac{1}{1-\frac{z+1}{1+i}}\]

Answer 5

It depends on the point around which you want to develop the function.

Answer 6

sorry, I mean the expansion point, English is not my native language, I hope you know what I mean