Resultant Gamma after Einstein velocity addition

[wil3]

Hello. Let's say that I am in a frame in which I see a rocket traveling at v. This rocket then fires a projectile forward with velocity u in its rest frame.

I can find u' easily enough using the Einstein velocity addition formula. However, I recall seeing a version of the formula that uses gammas instead(ie, if \gamma is defined for v and \Gamma is defined for u, then there is some compact equation for \Gamma' purely as a function of the other two gammas)

Does anyone know this formula? It is proving very difficult to derive. Thanks very much.

 

[ghwellsjr]

Could you be thinking of the Relativistic Doppler Factor where you can just multiply them for multiple velocities?

 

[wil3]

Nah, I remember this came up in class on a problem of this exact sort. I seem to remember there being a \Gamma*\gamma term going on somewhere. But thanks for the analysis-- I'm sure there is a parallel with the Doppler Effect.