arXiv:0801.1493 Abstract | arXiv Analytics

arXiv:0801.1493 [math.CA]Abstract References Reviews Resources

Differential Galois Theory of Linear Difference Equations

Published 2008-01-09Version 1

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 q-hypergeometric functions.

Comments: 50 pages

Categories: math.CA

Subjects: 12H05, 12H10, 33B15, 39A10, 39A15

Keywords: linear difference equations, differential galois theory, differential relationship holds, reprove hoelders theorem, gamma function satisfies

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