Gosper's Algorithm and Hypergeometric Solutions

Abstract

In this paper, we study Gosper's algorithm where we use Petkovšek’s technique togive a derivation for Gosper’s algorithm. We show that the least common multiplier can beused to give two simpler algebraically motivated approaches to find hypergeometricsolutions of linear recurrences with the additional restriction that the leading and trailingcoefficients are constant. In the second approach we use the universal denominator idea.The main result of these approaches that finding hypergeometric solutions reduces tofinding polynomial solutions.