晶格格林函数：d维面心立方晶格，d = 8，9，10，11，12
Lattice Green Functions: the d-dimensional face-centred cubic lattice, d=8, 9, 10, 11, 12
摘要：
我们以前报道的递归方法产生的$d$维面心立方晶格（fcc）的晶格格林函数的扩展。用该方法生成了d = 7时的多个系数，得到了相应的线性微分方程。本文通过对d = 8，9，10，11，12的级数和相应的线性微分方程组的产生，证明了该方法的强度和极限。这些线性微分方程的微分伽罗瓦群被证明是辛的d = 8，10，12和正交的d = 9，11。递归关系自然地提供了2维阵列$ T_d(n,j)$，其中只有系数$ t_d(n,0)$对应于d维fcc的晶格格林函数的系数。系数$ t_d(n,j)$与我们分析的线性偏微分方程所湮灭的D-有限二元级数相关联。
英文摘要：
We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding linear differential equation has been obtained. In this paper, we show the strength and the limit of the method by producing the series and the corresponding linear differential equations for d=8, 9, 10, 11, 12. The differential Galois groups of these linear differential equations are shown to be symplectic for d=8, 10, 12 and orthogonal for d= 9, 11. The recursion relation naturally provides a 2-dimensional array $ T_d(n,j)$ where only the coefficients $ t_d(n,0)$ correspond to the coefficients of the lattice Green function of the d-dimensional fcc. The coefficients $ t_d(n,j)$ are associated to D-finite bivariate series annihilated by linear partial differential equations that we analyze.
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