Differential Galois Theory of Linear Difference Equations
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 Hoelder'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 qhypergeometric functions.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 arXiv:
 arXiv:0801.1493
 Bibcode:
 2008arXiv0801.1493H
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 12H05;
 12H10;
 33B15;
 39A10;
 39A15
 EPrint:
 50 pages