Elliptic Hypergeometric Solutions to Elliptic Difference Equations - Magnus, A.P. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
It is shown how to define difference equations on particular lattices {xn}, n ∊ Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.