The Lauricella function and its relationship with other hypergeometric functions

The talk is focused on study of the relationship of the Lauricella function theory and the corresponding system of partial differential equations with the theory of the Horn hypergeometric functions and the Gelfand—Kapranov—Zelevinsky (GKZ) functions. The issue of the analytical continuation of the Lauricella series is also considered, which is one of the main ones also for the Horn and the GKZ functions. A general approach to solution of the analytical continuation problem for the Lauricella function is given and the set of corresponding formulas is presented.