community.
Found an example which seemingly easy but I cannot get the proper idea.
Consider absolute convergent $\forall z$ series $\sum_{n=0}^{\infty}c_{n}z^{n}$ . Since $z^k$ function can be considered as linearly independent, next problem can be formulated:
$\sum_{k=0}^{\infty}\alpha_{k}z^{k}=\left(\sum_{n=0}^{\infty}c_{n}z^{n}\right)^{N}$
Here $N$ - integer, $\alpha_k$ - unknown. The question is whether there is an easy way to find $\alpha_k$ at least up to some finite $k$? If there is no analytic way, I would like to know at least how to setup this problem on some programming language. I was thinking about multinomial theorem; however, this one isn't much applicable, as fas as I see.
Thanks in advance.