In this paper we give a new algorithm to compute Liouvillian solutions of linear difference equations. Compared to the prior algorithm by Hendriks and Singer, our main contribution consists of two theorems that significantly reduce the number of combinations that the algorithm will check.
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence equations and a counterpart to existing results on differential equations. As motivation and application for this work, we… (More)
The goal in this paper is to find closed form solutions for linear recurrence equations, by transforming an input equation <i>L</i> to an equation <i>L</i><sub><i>s</i></sub> with known solutions. The main problem is how to find a solved equation <i>L</i><sub><i>s</i></sub> to which <i>L</i> can be reduced. We solve this problem by computing local data at… (More)
The software is an implementation of the algorithms in , , and . The main algorithm from  is implemented with additional base equations beyond what appear in  and is incorporated into . Common to each algorithm is a transformation from a base equation to the input using transformations that preserve order and homogeneity (referred to as… (More)