I think you are looking for an nice clean way to write out the model equation or formula for the odds ratio, which I don't think are available. It is a bias correction in the likelihood, so I think the two above mention equations remain the same, but the interworkings for coefficient calculation are slightly tweaked.

I am a little like you, in that I know when to use it and I interpret results the same as before but document the use of the correction. The best that I can do is provide the link below and say perhaps some people (unsure?) add a subscript documenting its use (e.g., ORFirth: 2.4 95% CI: 1.2, 3.9), imagine I know Latex and the firth is a subscript.

http://stats.stackexchange.com/quest...tic-regression

PS, We can see if anyone else chimes in, and please update you post if you figure out an acceptable solution.