Exact evaluation of the Baxter-Bazhanov Green function

摘要

The analytic properties of the lattice Green function [GRAPHICS] where t lies in a complex plane which is cut along the real axis from -2 to +2, are investigated. In particular, it is proved that tG(t) can be written in the product form [GRAPHICS] where xi = 2/t and F-2(1)(a, b; c; z) denotes a hypergeometric function. This result and the analytic continuation formulae for the F-2(1) function are then used to obtain various exact closed-form expressions for the related functions [GRAPHICS] where s epsilon (-2, 2). It is also shown that G(t) is a solution of a third-order Fuchsian differential equation. [References: 12]