We discuss two algorithms which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, construct a finite set M of polynomials, irreducible in k[x], such that if the given equation has a solution F(x)@...
A normal form is given for integrable linear difference-differential equations {@s(Y)=AY,@d(Y)=BY}, which is irreducible over C(x,t) and solvable in terms of Liouvillian solutions. We refine this normal form and devise an algorithm to compute all ...
Let L(y) = b be a linear differential equation with coefficients in a differential field k, of characteristic 0, We show that if L(y) = b has a non-zero solution Liouvillian over k, then either L(y) = 0 has a non-zero solution u such that u'/u is ...
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