Middle convolution and the hypergeometric equation

The addition and the Detweiler and Reiter algebraic analogue of Katz's middle convolution are certain transformations of Fuchsian systems. Their compositions are useful to get nontrivial relations between solutions of these systems. The aim of this paper is to study the result of these transformations for a 2 x 2 linear Fuchsian system with triangular matrices and four singularities; the isomonodromy deformations of which are given by the hypergeometric functions.