Table 3: Basic spectral transformation equations.
\begin{displaymath}\nu = \frac{c}{\lambda}\end{displaymath} (6)
\begin{displaymath}\frac{{\rm d}\nu}{{\rm d}\lambda} = -\frac{c}{\lambda^2}\end{displaymath} (7)
\begin{displaymath}\nu = \nu_0 \frac{c - \varv}{\sqrt{c^2 - \varv^2}}\end{displaymath} (8)

\begin{displaymath}\frac{{\rm d}\nu}{{\rm d}\varv} = -\frac{c\nu_0} {(c+\varv) \sqrt{c^2-\varv^2}}\end{displaymath} (9)
\begin{displaymath}\lambda = \frac{c}{\nu}\end{displaymath} (10)

\begin{displaymath}\frac{{\rm d}\lambda}{{\rm d}\nu} = -\frac{c}{\nu^2}\end{displaymath} (11)
\begin{displaymath}\lambda = \lambda_0 \frac{c + \varv}{\sqrt{c^2 - \varv^2}}\end{displaymath} (12)

\begin{displaymath}\frac{{\rm d}\lambda}{{\rm d}\varv} = \frac{c\lambda_0} {(c - \varv)
\sqrt{c^2 - \varv^2}}\end{displaymath} (13)
\begin{displaymath}\varv= c \frac{\nu_0^2 - \nu^2}{\nu_0^2 + \nu^2}\end{displaymath} (14)

\begin{displaymath}\frac{{\rm d}\varv}{{\rm d}\nu} = -\frac{4c\nu\nu_0^2}{(\nu^2 + \nu_0^2)^2}\end{displaymath} (15)
\begin{displaymath}\varv= c \frac{\lambda^2-\lambda_0^2} {\lambda^2+\lambda_0^2}\end{displaymath} (16)

\begin{displaymath}\frac{{\rm d}\varv}{{\rm d}\lambda} = \frac{4c\lambda\lambda_0^2}
{(\lambda^2 + \lambda_0^2)^2}\end{displaymath} (17)


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