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.