I have two polynomials:
$Q(z)=q_0 +q_1 z + \cdots q_mz^m$ and its reflection $ Q^'(z)=q_0 z^m +q_1z^{m-1}+ \cdots q_m$. I'd like to find a relation between them (i.e. $Q(z)= \phi(Q'(z))$, so far for I could only show that for $Q(z)=q_0+q_1 z$ and $Q'(z)=q_0z+q_1$ $Q^2(z)-Q'^2(z)=(1-z^2)(q_0^2-q_1^2)$.
There is probably some well-known solution to this problem. Please don't solve it for me, just point in the right direction.