\begin{equation}
P_{\nu}=\left<\nu\left|P(q)\right|\nu\right>_q = P^{[0]}
+ \frac{1}{2}P^{[2]}\left(\frac{\hbar}{\mu\omega_e}\right)\left(\nu+\frac{1}{2}\right)
   -\frac{1}{2}P^{[1]}E^{[3]}\left(\frac{\hbar}{\mu\omega_e}\right)^2\frac{\left(\nu+\frac{1}{2}\right)}{\hbar\omega_e}+\ldots
\end{equation}