\begin{aligned} z^{'} & = \frac{z - u t}{\sqrt{1 - (\frac{u}{c})^{2}}} \\ y^{'} & = y \\ x^{'} & = x \\ t^{'} & = \frac{t - \frac{u z}{c^{2}}}{\sqrt{1 - (\frac{u}{c})^{2}}} \end{aligned}

${\begin{align*}z' &=\frac{z-ut}{\sqrt{1-(\frac{u}{c})^2 }} \\ y' &= y \\ x' &= x \\ t'&=\frac{t- \frac{uz}{c^2}}{ \sqrt{1-(\frac{u}{c})^2}} \end{align*}}$

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