This band shape is described by the function: \[F\left(\nu - \nu _{0}\right) = \frac{1}{\pi }\ \gamma \ ((\nu - \nu _{0})^{2}+\gamma ^{2})^{-1}\] where v 0 is the mean band position, γ is the half band width at half maximum, and F(ν - ν0) is the frequency distribution function.