Rational interpolation to solutions of Riccati difference equations on elliptic lattices

It is shown how to define difference equations on particular lattices { x n } , n ∈ Z , where the x n s are values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations (elliptic Riccati equations) have remarkable simple (!) interpolatory continued fraction expansions.