# Finite Singularities and Hypergeometric Solutions of Linear
Recurrence Equations

This paper introduces a new concept of finite singularities that is useful
for studying difference equations.
For example, in theorems 2 and 3 I use this concept prove new results on
the algebraic extensions one needs for solving operators of
order 2 and 3. These two theorems are examples of what
one can do with this concept of finite singularities.
For the case order>3, and for more details and explicit examples
on finite singularities, see the paper
"Computing Hypergeometric Solutions of Linear Recurrence Equations"
which can be found here.
The algorithm given in the paper has now been implemented.
Here is a version for Maple6
(source code)
and a comparison.
Note that this code is now part of Maple 9 (hypergeomsols in LREtools).
For related ideas, additional explanations, and examples see:
Download this paper.