I am aware of some of the history of the gamma function $\Gamma(z)$, partly through
a 2009(!) MO question "[Who invented the gamma function?](https://mathoverflow.net/a/9790/6094)"—Euler, Bernoulli, etc.
My question does not seem to be answered in that discussion, or in other historical accountings I can easily locate: 



> 
> ***Q***. Why was the symbol $\Gamma$ chosen for the generalized factorial?
> 
> 
> 


Were $\alpha(z)$ and $\beta(z)$ already "taken" and so $\Gamma$ was a natural successor?
Or was the choice due to the shape of the uppercase $\Gamma$?
Or some other reason? Or lost to history?



Why does the gamma function use the symbol $\Gamma(\,)$?
The first use of $\Gamma$ in this sense is due to Legendre (1811). It is unknown why he choose that notation but some speculations are recorded at <http://jeff560.tripod.com/functions.html> 


They range from the Gamma being an inverted L (from Legendre) and variants, to the in my opinion more integresting that the logarithm of $\Gamma$ is related to the Euler-Mascheroni constant, which is mentioned in that work of Legendre and was (then) denoted $C$ (which makes $\Gamma$ as a Greek capital C natural) or also $\gamma$ (that usage was present before the work of Legendre too).


