# Differential Galois theory of linear difference equations

@article{Hardouin2008DifferentialGT, title={Differential Galois theory of linear difference equations}, author={C. Hardouin and M. Singer}, journal={Mathematische Annalen}, year={2008}, volume={342}, pages={333-377} }

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.

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