I'm looking at some non-commuting operators $A, B$ say and I'm interested in their exponential $e^{A + B}$ or formulas for binomial expansions like $(A + B)^n$ when the operators have a nice commutation relation. I'm new to this and I'd like any references or formulas (I'm aware for instance of the Baker-Hausdorff-Campbell formula but that's about it) for the case when $AB = cBA$ for some constant $c$ which generalises the commutative case $c = 1$. Are there any known formulas for binomial coefficients (e.g. the coefficient on $A^kB^{n-k}$ assuming all terms that can be, have been, brought into this form using the commutation relation) or the exponential?
I've tried to use the BHC formula but I haven't had much success in simplifying my results into something tractable - the same goes for the binomial coefficients, where I can find a recursive formula for them but I can't really simplify them.
Thanks if anyone knows any good references for formulas.
EDIT: I'll leave the question open but I have found that in some references the commutation relation $AB = qBA$ is called $q$-commuting.