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Mathematische Annalen

, Volume 342, Issue 2, pp 333–377 | Cite as

Differential Galois theory of linear difference equations

  • Charlotte Hardouin
  • Michael F. SingerEmail author
Article

Abstract

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hölder’s theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric equations.

Keywords

Difference Equation Algebraic Group Galois Group Galois Theory Differential Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.IWRHeidelbergGermany
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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