For the Lauricella hypergeometric function $F_D^{(N)}$ with an arbitrary number of variables $z_1,\dots ,z_N$, we construct formulas for analytic continuation into the vicinity of hyperplanes $\{z_j=z_l\}$ and their intersections providing that all variables are close to unit. Such formulas represent the function $F_D^{(N)}$ near the point $(1,\dots ,1)$ as linear combinations of N–multiple hypergeometric series that are solutions of the same system of partial differential equations as $F_D^{(N)}$. Such series are the N–dimensional analog of the Kummer solutions known for the Gauss equation. The constructed analytical continuation formulas allow one to effectively calculate the function $F_D^{(N)}$ outside the unit polydisk.

对于 Lauricella 超几何函数$F_D^{(ñ)}$具有任意数量的变量$z_1,\dots ,z_{ñ}$，我们构造了超平面附近的解析延拓公式$\{z_j=z_l\}$以及它们的交点，前提是所有变量都接近单位。这样的公式代表函数$F_D^{(ñ)}$靠近点$(1,\dots ,1)$作为N - 多个超几何级数的线性组合，它们是相同的偏微分方程组的解$F_D^{(ñ)}$. 这样的级数是高斯方程已知的 Kummer 解的N维模拟。构造的解析延拓公式允许有效地计算函数$F_D^{(ñ)}$在单位 polydisk 之外。