  We consider the notions of operator-valued infinitesimal (OVI) free
independence, OVI Boolean independence, and OVI monotone independence. For each
notion of OVI independence, we introduce the corresponding infinitesimal
transforms, and then we show that the transforms satisfy certain multiplicative
property. Additionally, we extend the concept of $t$-coefficients to the
infinitesimal framework and investigate its properties. Finally, we present an
application involving complex Wishart matrices utilizing our infinitesimal free
multiplicative formula.

Operator Algebras