if $u$ and ${u}^{\beta \x80\xb2}$ are a velocity referred to two inertial frames with relative velocity $v$ confined to the $x$ axis, then the quantities $l$, $m$, $n$ defined by

$(l,m,n)=\frac{1}{|u|}({u}_{x},{u}_{y},{u}_{z})$

and

$({l}^{\beta \x80\xb2},{m}^{\beta \x80\xb2},{n}^{\beta \x80\xb2})=\frac{1}{|{u}^{\beta \x80\xb2}|}({u}_{x}^{\beta \x80\xb2},{u}_{y}^{\beta \x80\xb2},{u}_{z}^{\beta \x80\xb2})$

are related by

$({l}^{\beta \x80\xb2},{m}^{\beta \x80\xb2},{n}^{\beta \x80\xb2})=\frac{1}{D}(l\beta \x88\x92\frac{v}{u},m{\mathrm{\Xi \xb3}}^{\beta \x88\x921},n{\mathrm{\Xi \xb3}}^{\beta \x88\x921})$

and that this can be considered a relativistic aberration formula. The author gives the following definition for $D$, copied verbatim.

$D=\frac{{u}^{\beta \x80\xb2}}{u}(1\beta \x88\x92\frac{{u}_{x}v}{{c}^{2}})={[1\beta \x88\x922l\frac{v}{u}+\frac{{v}^{2}}{{u}^{2}}\beta \x88\x92(1\beta \x88\x92{l}^{2})\frac{{v}^{2}}{{c}^{2}}]}^{\frac{1}{2}}$

Why is that better than the second expression?

Also, in case it's not clear, $\mathrm{\Xi \xb3}=1/\sqrt{1\beta \x88\x92\frac{{v}^{2}}{{c}^{2}}}$ and $|u|=|({u}_{x},{u}_{y},{u}_{z})|=\sqrt{{u}_{x}^{2}+{u}_{y}^{2}+{u}_{z}^{2}}$