Exact product forms for the simple cubic lattice Green function II

The analytical properties of the lattice Green function [GRAPHICS] are investigated, where n is an integer and w is a complex variable. In particular, it is shown that G(2n, n, n; w) is a solution of a fourth-order linear differential equation of the Fuchsian type. From this differential equation it is found that G(2n, n, n; w) can be evaluated in terms of a product of two Heun functions {H-j (n, v) j = 1, 2}, where [GRAPHICS] and (a)(n) denotes the Pochhammer symbol. This formula is valid for varying values of w in the neighbourhood of w = infinity, provided that the argument function eta(+)(w) does not take real values in the interval (1, +infinity). Finally, this F-2(1) product form is used to determine the asymptotic behaviour of G(2n, n, n; w) as n --> infinity.