Jacobi-type differential relations for the Lauricella function FD (N)

For the generalized Lauricella hypergeometric function FD (N), Jacobi-type differential relations are obtained and their proof is given. A new system of partial differential equations for the function FD (N) is derived. Relations between associated Lauricella functions are presented. These results possess a wide range of applications, including the theory of Riemann–Hilbert boundary-value problem. © 2016, Pleiades Publishing, Ltd.