Rational interpolation to solutions of Riccati difference equations on elliptic lattices

It is shown how to define difference equations on particular lattices {xn}, n ∈ Z, where the xns 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. 1. Difference equations and lattices. Simplest difference equations relate two values of the unknown function f : say, f(φ(x)) and f(ψ(x)). Most instances [19] are (φ(x), ψ(x)) = (x, x + h), or the more symmetric (x − h/2, x + h/2), or also (x, qx) in q−difference equations [7, 11, 12]. Recently, more complicated forms (r(x) − √