Holonomic Difference Equations and Asymptotic Expansion
As we have seen in Chapter 1, the Γ-function is a solution of a first-order difference equation which can be uniquely determined by its asymptotic behavior at infinity. This fact can be generalized to the cases of several variables that contain a finite number of unknown meromorphic functions which satisfy a holonomic system of difference equations. The hypergeometric functions discussed in Chapters 2 and 3 satisfy holonomic systems of difference equations with respect to the parameters α = (α1, …, α m ). Their asymptotic structure at infinity strongly reflects topological aspects of their twisted de Rham (co)homology.