Analytic continuation of Lauricella's function FD(N) for large in modulo variables near hyperplanes {zj = zl)

We consider the La uricella hypergeometric function F-D((N)), depending on N >= 2 variables z(1), ..., z(N), and obtain formulas for its analytic con- tinuation into the vicinity of a singular set which is an intersection of the hyperplanes {z(j) = z(l)}. It is assumed that all N variables are large in modulo. This formulas represent the function F-D((N)) outside of the unit polydisk in the form of linear combinations of other N-multiple hypergeometric series that are solutions of the same system of partial differential equations as F-D((N)). The derived hypergeometric series are N-dimensional analogues of the Kummer solutions that are well known in the theory of the classical hypergeometric Gauss equation.