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.
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)
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)