What is the General Expression for the Product of Two Matrix Exponentials?

[dipole]

Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices?

i.e. something of the form,
$$e^Ae^B = e^{( * )}$$

where the ( * ) would, I assume, depend in some way on the commutator $[A,B]$?

I can only find examples online when $[A,B] = 0$ which is rather trivial, but nothing about the more general case...

 

[micromass]

Baker-Campbell-Hausdorff formula: http://en.wikipedia.org/wiki/Baker–Campbell–Hausdorff_formula#Matrix_Lie_group_illustration