A simple algorithm is suggested for the construction of a polynomial divisible by the denominator of any rational solution of the linear difference equation.Expand

Linear differential and difference equations whose coefficients and right-hand sides are polynomials are considered. The problem of constructing all rational solutions of an equation is solved.

The algorithm described here extends the algorithm to nd all polynomial solutions of di erential and di erence equations that was given in [1, 2] to more general operators.Expand

We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties.Expand

We describe a new direct algorithm for transforming a linear system of recurrences into an equivalent one with nonsingular leading or trailing matrix.Expand

We present an algorithm which, given a hypergeometric term <i>T</i>(<i>n</i>), constructs hypergeometry terms <i T</i><subscrpt>1</subscRpt>(< i>N</i>) such that the sum of the terms is minimal in some sense.Expand

D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals of hyperexponential functions.Expand