The Boolean quadratic forms and tangent law . (część II)

I will talk about the limit of weighted sums of Boolean commutators and anticommutators and I will show that the shifted generalized tangent function appears in a limit theorem. In the way of proof I will present a formula for the Boolean cumulants of quadratic forms which exhibits an interesting connection to the isomorphism between interval partitions of r+1 elements with special kind of interval partitions of 2r points. I will show that this result can be apply to obtain a several theorems about quadratic forms in the Boolean probability theory.