Holonomic Difference Equations and Asymptotic Expansion

Part of the Springer Monographs in Mathematics book series (SMM)


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.


Asymptotic Expansion Difference Equation Meromorphic Function Hypergeometric Function Morse Theory 
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© Springer 2011

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan

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