Lattice Green's function for the simple cubic lattice in terms of a Mellin-Barnes type integral. II

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Abstract
The series representation of the lattice Green's function for the simple cubic lattice I(a)=π−3∫oπ∫oπ∫oπD−1dxdydz, where D=a-iε-cosx-cosy-cosz, around the singularity a=1 is obtained in fractional powers of a2−1 (convergent for |a2−1|<1), by the method of analytic continuation using a Mellin-Barnes type integral and also by use of the analytic continuation of 3F2 (, , ; , ; 1) as a function of the parameter. It gives leading and full expansions near the singularity a=1.