Differential Galois Theory of Linear Difference Equations

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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.
50 pages

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Classical Analysis and ODEs, 12H05, 12H10, 33B15, 39A10, 39A15

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http://salesiana.dossiersoluciones.com/handle/123456789/145663

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.1493
 http://arxiv.org/abs/0801.1493

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arXiv