We assume that the conditions of question 12 are satisfied and that $\lambda(0) \neq 0$. Show that $E \circ F = F \circ E + H - H^{-1}$ if and only if for all $i \in \mathbf{Z}$, $$\mu(i) = \mu(i-1) + \lambda(0) q^{-2i} - \lambda(0)^{-1} q^{2i}$$
We assume that the conditions of question 12 are satisfied and that $\lambda(0) \neq 0$. Show that $E \circ F = F \circ E + H - H^{-1}$ if and only if for all $i \in \mathbf{Z}$,
$$\mu(i) = \mu(i-1) + \lambda(0) q^{-2i} - \lambda(0)^{-1} q^{2i}$$