Free probability for pairs of faces III: 2-Variables bi-free partial S- and T-transforms

We introduce two 2-variables transforms: the partial bi-free S-transform and the partial bi-free T-transform. These transforms are the analogues for the bi-multiplicative and, respectively, for the additive–multiplicative bi-free convolution of the 2-variables partial bi-free R-transform in our previous paper in this series.