Converging to Gosper's Algorithm

TL;DR

This paper uncovers a convergence property related to GCDs of factorials and introduces a unified method for computing universal denominators in rational solutions of linear difference equations, enhancing Gosper's and Abramov's algorithms.

Contribution

It presents a new convergence property and a unified approach to compute universal denominators for rational solutions, improving existing algorithms.

Findings

Identifies a convergence property of GCDs of factorials.

Develops a unified method for universal denominator computation.

Enhances Gosper's and Abramov's algorithms.

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.