You are right, that I am wrong. You see, I can accept when I have made a mistake :P

I would be interested to see how you got to:

[tex]\gamma(v')=\gamma(v) \gamma(u) (1+v_xu/c^2)[/tex]

from:

[tex]v'^2=v'_x^2+v'_y^2[/tex]

[tex]v'_x=\frac{v_x+u}{1+v_xu/c^2}[/tex]

[tex]v'_y=\frac{v_y \sqrt{1-u^2/c^2}}{1+v_xu/c^2}[/tex]