Hausdorff formula for anticommutation

hello. it's the first time I use this site I hope that I find the answer of my question: does the hausdorff formula for anti commutation have the same formula for commutation?

I think the sign of the two exponentials must be positive,is it correct?
exp(A) B exp(A)= B + {A,B} + {A,{A,B}} +.....

strangerep
hello. it's the first time I use this site I hope that I find the answer of my question: does the hausdorff formula for anti commutation have the same formula for commutation?
If A and B are anti-commuting quantities, then I presume you also mean ##A^2=0 =B^2## ?

If so, then ##\exp(A) = 1 + A## (since higher order powers vanish). That simplifies all formulas considerably...