Liouvillian Solutions of Difference-Differential Equations

Details Liouvillian Solutions of Difference-Differential Equations Liouvillian Solutions of Difference-Differential Equations

2008-10-09

arxiv.org/abs/0810.1574v1

Computer Science

Symbolic Computation

53 pages

Scientific paper

For a field k$with an automorphism \sigma and a derivation \delta, we introduce the notion of liouvillian solutions of linear difference-differential systems {\sigma(Y) = AY, \delta(Y) = BY} over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x,t), \sigma(x) = x+1, \delta = d/dt$ and the size of the system is a prime.

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