  Suppose V{\nu} is the pseudo-variance function of the Cauchy-Stieltjes Kernel
(CSK) family K+({\nu}) generated by a non degenerate probability measure {\nu}
with support bounded from above. We determine the formula for pseudo-variance
function (or variance function V{\nu} in case of existence) under boolean
additive convolution power. This formulas is used to identify the relation
between variance functions under Boolean Bercovici-Bata Bijection between
probability measures. We also gives the connection between boolean cumulants
and variance function and we relate boolean cumulants of some probability
measures to Catalan numbers and Fuss Catalan numbers.
