Let $A$ and $B$ be two (not necessarily commuting) matrices of order $n$. Then
$$\mathop{\lim}\limits_{t \to 0}e^{-tB}e^{-tA}e^{tB}e^{tA} = e^{t^2[B,A] + o(t^3)}$$
I recall coming across this formula at various times but can't seem to find a reference for it. Is there a recognized name for it?