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 give a new algorithm to compute Liouvillian solutions of linear difference equations. The first algorithm for this was given by Hendriks in 1998, and Hendriks and Singer in 1999. Several improvements have been published, including a paper by Cha and van Hoeij that reduces the combinatorial problem. But the number of combinations still… (More)
The Graduate School has verified and approved the above-named committee members. ii To my parents, Henry and Ann Levy iii ACKNOWLEDGEMENTS I would like to thank my advisor Mark van Hoeij for his support, patience, and friendship. I would also like to thank the members of my committee for being so approachable and free with their time.