Abstract:  Given two polynomials, we find a convergence property of the GCD of the rising factorial and the falling factorial. Based on this property, we present a unified approach to computing the universal denominators as given by Gosper's algorithm and Abramov's algorithm for finding rational solutions to linear difference equations with polynomial coefficients.

  AMS Classification:  33F10; 05A19.

  Keywords:  Gosper's algorithm, Abramov's algorithm, universal denominator.

  Download:  Pdf