We consider the Lauricella hypergeometric function $F_D^{(N)}$, depending on $N\ge 2$ variables $z_1,\dots ,z_N$, and obtain formulas for its analytic continuation 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.

我们考虑 Lauricella 超几何函数$F_D^{(ñ)}$， 根据$ñ\ge 2$变量$z_1,\dots ,z_{ñ}$, 并获得其解析延拓到作为超平面交集的奇异集附近的公式$\{z_j=z_l\}$. 假设所有N个变量在模上都很大。此公式表示函数$F_D^{(ñ)}$以其他N多超几何级数的线性组合形式存在于单位 polydisk 之外，这些超几何级数是相同的偏微分方程组的解$F_D^{(ñ)}$. 导出的超几何级数是经典超几何高斯方程理论中众所周知的 Kummer 解的N维类似物。