ν′ = ν ∗ \frac{1}{1 ∓ \frac{v}{c}}

λ′ = λ ∗ (1 ∓ \frac{v}{c})

ν′ = ν ∗ \frac{1}{1 ∓ \frac{v}{c}} ∗ \frac{1}{γ}

ν′ = ν ∗ \begin{matrix}√ & \overline{1 − v/c} \\ √ & \overline{1 + v/c} \end{matrix}

λ′ = λ ∗ \begin{matrix}√ & \overline{1 + v/c} \\ √ & \overline{1 − v/c} \end{matrix}

λ_{direct} = λ ∗ (1 − v/c) = λ − (λ ∗ \frac{v}{c})

λ_{reflect} = λ ∗ (1 + v/c) = λ + (λ ∗ \frac{v}{c})

λ_{direct} = λ ∗ (1 − \frac{v}{c} + \frac{1}{2} \frac{v^{2}}{c^{2}} ) = λ − (λ ∗ \frac{v}{c}) + (λ ∗ \frac{1}{2} \frac{v^{2}}{c^{2}} )

λ_{reflect} = λ ∗ (1 + \frac{v}{c} + \frac{1}{2} \frac{v^{2}}{c^{2}} ) = λ + (λ ∗ \frac{v}{c}) + (λ ∗ \frac{1}{2} \frac{v^{2}}{c^{2}} )

ν′ = ν ∗ \frac{1}{γ}

λ′ = λ ∗ γ