$$
   \nu^\prime = \nu * { { 1 } \over { 1 \mp {{v}\over{c}} } }
$$

$$
   \lambda^{\prime} = \lambda * ( 1 \mp {{v} \over {c}} )
$$


$$
   \nu^\prime = \nu * { { 1 } \over { 1 \mp {{v}\over{c}} } } * { {1}\over{\gamma}}
$$

$$
   \nu^\prime = \nu * { {\sqrt{1 - v/c}}\over{\sqrt{1 + v/c}}}
$$
  
$$
   \lambda^\prime = \lambda * { {\sqrt{1 + v/c}}\over{\sqrt{1 - v/c}}}
$$

$$
   \lambda_{\rm direct} = \lambda * (1 - v/c)  = \lambda - 
                                               ( \lambda*{{v}\over{c}} )
$$

$$
   \lambda_{\rm reflect} = \lambda * (1 + v/c)  = \lambda + 
                                               ( \lambda*{{v}\over{c}} )
$$

$$
   \lambda_{\rm direct} = \lambda * (1 - {v\over{c}} + {{1}\over{2}}{{v^2}\over{c^2}})
                        = \lambda - ( \lambda*{{v}\over{c}} ) 
                                + ( \lambda*{{1}\over{2}}{{v^2}\over{c^2}} )
$$

$$
   \lambda_{\rm reflect} = \lambda * (1 + {v\over{c}} + {{1}\over{2}}{{v^2}\over{c^2}})
                        = \lambda + ( \lambda*{{v}\over{c}} ) 
                                + ( \lambda*{{1}\over{2}}{{v^2}\over{c^2}} )
$$

$$
   \nu^\prime = \nu * { {1}\over{\gamma}}
$$

$$
   \lambda^\prime = \lambda * \gamma
$$



\bye
