10.8.13 Series with complex terms
condition: Find all Laurent expansions of this function in powers \( \left(z-z_{0}\right) \) : \[ \frac{2 z-i}{(z+i)(z-2 i)}, \quad z_{0}=-i \text {. } \]
Expansion of complex functions in Laurent and Taylor series. Both single-valued and multi-valued functions are considered, indicating the branches along which the multi-valued functions are taken.