Galois groups of linear difference-differential equations (Q2693367)

In the present paper, the authors study family of differential/difference equations. One considered example is the Chebychev polynomials. The authors consider the specialisation of the differential (resp. difference) Galois group. Let \(C_1\) and \(C_2\) be the two specializations. They show that almost all groups in \(C_1 \cup C_2\) are algebraic subgroups of \(G\), the Galois group of the differential/difference system, and there is a nonempty subset of \(C_1\) and a nonempty subset of \(C_2\) such that \(G\) is the product of any pair of groups from these two subsets. These results should have applications in the computation of \(G\).