$\mathcal{P}$ denotes the vector space of polynomial functions with complex coefficients. We denote for every pair $(P,Q) \in \mathcal{P}^2$,
$$\langle P, Q \rangle = \int_0^{+\infty} e^{-t}\bar{P}(t)Q(t)\,dt.$$
Verify that $\langle \cdot, \cdot \rangle$ defines an inner product on $\mathcal{P}$.