# Definition The Lie Product Formula is the following identity: $ e^{X+Y} = \lim_{m \rightarrow \infty} \left(e^{\frac{X}{m}} e^{\frac{Y}{m}}\right)^m $ where $X, Y$ are elements of some [[Lie Algebra]] $\mathfrak{g}$. We can think of this formula as expression addition in $\mathfrak{g}$ in terms of multiplication in the [[Lie group]] $G$. # Proof