Solving Difference Equations in Finite Terms

@article{Hendricks1999SolvingDE,
  title={Solving Difference Equations in Finite Terms},
  author={P. A. Hendricks and Michael F. Singer},
  journal={J. Symb. Comput.},
  year={1999},
  volume={27},
  pages={239-259}
}
One of the main results in the Galois theory of linear differential equations is that the Galois group of an equation L(y) = 0 has a solvable subgroup of finite index iff the equation can be solved in terms of Liouvillian functions, that is, in terms of functions built up from the coefficients of L(y) iterating field operations, differentiation, integration, exponentials of integrals and taking roots of polynomials (see Kaplansky (1976), Kolchin (1948), Kolchin (1976), Magid (1994… CONTINUE READING
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