Liouvillian solutions of irreducible linear difference equations

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.

[1]  Marko Petkovsek,et al.  Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficents , 1992, J. Symb. Comput..

[2]  Marius van der Put,et al.  Galois Theory of Difference Equations , 1997 .

[3]  Moulay A. Barkatou,et al.  Rational solutions of matrix difference equations: the problem of equivalence and factorization , 1999, ISSAC '99.

[4]  Peter A. Hendriks,et al.  Solving Difference Equations in Finite Terms , 1999, J. Symb. Comput..

[5]  Mark van Hoeij,et al.  Finite singularities and hypergeometric solutions of linear recurrence equations , 1999 .

[6]  David Jagerman.  Linear Difference Equations with Polynomial Coefficients , 2000 .

[7]  Raphaël Bomboy.  Réductibilité et résolubilité des équations aux différences finies , 2001 .

[8]  Manuel Bronstein,et al.  On solutions of linear functional systems , 2001, ISSAC '01.

[9]  Mark van Hoeij,et al.  Computing Hypergeometric Solutions of Linear Recurrence Equations , 2006, Applicable Algebra in Engineering, Communication and Computing.

[10]  Moulay A. Barkatou,et al.  Apparent singularities of linear difference equations with polynomial coefficients , 2005, Applicable Algebra in Engineering, Communication and Computing.

[11]  Denis E. Khmelnov.  Search for Liouvillian solutions of linear recurrence equations in the MAPLE computer algebra system , 2008, Programming and Computer Software.

[12]  Moulay A. Barkatou,et al.  On m-Interlacing Solutions of Linear Difference Equations , 2009, CASC.

[13]  Michael F. Singer,et al.  Liouvillian solutions of linear difference-differential equations , 2008, J. Symb. Comput..