Liouvillian solutions of linear difference–differential equations

• Published in: Journal of symbolic computation Vol. 45; no. 3; pp. 287 - 305
• Main Authors: Feng, Ruyong, Singer, Michael F., Wu, Min
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2010
• Subjects: Galois theory; Linear difference–differential equations; Liouvillian sequences; Liouvillian sequences; Linear difference–differential equations; Galois theory

For a field k with an automorphism σ and a derivation δ , we introduce the notion of Liouvillian solutions of linear difference–differential systems { σ ( Y ) = A Y , δ ( Y ) = B Y } over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the fo...