Table 4: Extended spectral transformation equations.

$\begin{displaymath}\nu = \nu_0 \left(1 - \frac{V}{c}\right)\end{displaymath}$ (18)

$\begin{displaymath}\frac{{\rm d}\nu}{{\rm d}V} = -\frac{\nu_0}{c}\end{displaymath}$ (19)

$\begin{displaymath}V = c \frac{\nu_0 - \nu}{\nu_0}\end{displaymath}$ (20)

$\begin{displaymath}\frac{{\rm d}V}{{\rm d}\nu} = -\frac{c}{\nu_0}\end{displaymath}$ (21)

$\begin{displaymath}\nu = E / h\end{displaymath}$ (22)

$\begin{displaymath}\frac{{\rm d}\nu}{{\rm d}E} = 1 / h\end{displaymath}$ (23)

$\begin{displaymath}E = h \nu\end{displaymath}$ (24)

$\begin{displaymath}\frac{{\rm d}E}{{\rm d}\nu} = h\end{displaymath}$ (25)

$\begin{displaymath}\nu = c \kappa\end{displaymath}$ (26)

$\begin{displaymath}\frac{{\rm d}\nu}{{\rm d}\kappa} = c\end{displaymath}$ (27)

$\begin{displaymath}\kappa = \nu / c\end{displaymath}$ (28)

$\begin{displaymath}\frac{{\rm d}\kappa}{{\rm d}\nu} = 1 / c\end{displaymath}$ (29)

$\begin{displaymath}\lambda = \lambda_0 \left(1 + \frac{Z}{c}\right)\end{displaymath}$ (30)

$\begin{displaymath}\frac{{\rm d}\lambda}{{\rm d}Z} = \frac{\lambda_0}{c}\end{displaymath}$ (31)

$\begin{displaymath}Z = c \frac{\lambda - \lambda_0}{\lambda_0}\end{displaymath}$ (32)

$\begin{displaymath}\frac{{\rm d}Z}{{\rm d}\lambda} = \frac{c}{\lambda_0}\end{displaymath}$ (33)

$\begin{displaymath}\lambda = \lambda_0 (1 + z)\end{displaymath}$ (34)

$\begin{displaymath}\frac{{\rm d}\lambda}{{\rm d}z} = \lambda_0\end{displaymath}$ (35)

$\begin{displaymath}z = \frac{\lambda - \lambda_0}{\lambda_0}\end{displaymath}$ (36)

$\begin{displaymath}\frac{{\rm d}z}{{\rm d}\lambda} = \frac{1}{\lambda_0}\end{displaymath}$ (37)

$\begin{displaymath}\varv= c \beta\end{displaymath}$ (38)

$\begin{displaymath}\frac{{\rm d}\varv}{{\rm d}\beta} = c\end{displaymath}$ (39)

$\begin{displaymath}\beta = \varv/ c\end{displaymath}$ (40)

$\begin{displaymath}\frac{{\rm d}\beta}{{\rm d}\varv} = 1 / c\end{displaymath}$ (41)

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