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We previously reported on a recursive method to generate the expansion of thelattice Green function of the $d$-dimensional face-centred cubic lattice (fcc).The method was used to generate many coefficients for d=7 and the correspondinglinear differential equation has been obtained. In this paper, we show thestrength and the limit of the method by producing the series and thecorresponding linear differential equations for d=8, 9, 10, 11, 12. Thedifferential Galois groups of these linear differential equations are shown tobe symplectic for d=8, 10, 12 and orthogonal for d= 9, 11. The recursionrelation naturally provides a 2-dimensional array $ T_d(n,j)$ where only thecoefficients $ t_d(n,0)$ correspond to the coefficients of the lattice Greenfunction of the d-dimensional fcc. The coefficients $ t_d(n,j)$ are associatedto D-finite bivariate series annihilated by linear partial differentialequations that we analyze.

Lattice Green Functions: the d-dimensional face-centred cubic lattice, d=8, 9, 10, 11, 12