  Lattice Green functions appear in lattice gauge theories, in lattice models
of statistical physics and in random walks. Here, space coordinates are treated
as parameters and series expansions in the mass are obtained. The singular
points in arbitrary dimensions are found. For odd dimensions these are branch
points with half odd-integer exponents, while for even dimensions they are of
the logarithmic type. The differential equations for one, two and three
dimensions are derived, and the general form for arbitrary dimensions is
indicated. Explicit series expressions are found in one and two dimensions.
These series are hypergeometric functions. In three and higher dimensions the
series are more complicated. Finally an algorithmic method by Vohwinkel,
Luscher and Weisz is shown to generalize to arbitrary anisotropies and mass.
