How can I find asymptotic expansion of the function $(\text{log}(1+z))^2$ with respect to the asymptotic scale $\{z^{-m}, z^{-n}\text{log}(z), z^{-p}\text{log}^2(z), m,n,p=0,1,2,...\}$ while $z\rightarrow\infty$, $|\text{arg}(z)|<\pi$?
Thank you in advance.