Rational Generating Function Applications in Maple

Abstract

Generating function techniques have been used throughout the literature to evaluate summations and recurrences. Rational generating functions are a particularly effective computation tool, as they encode all linear recurrence sequences. These are sequences defined by homogeneous linear recurrences with constant coefficients. There are known generating function techniques for evaluating summations and convolutions that involve linear recurrence sequences. Unfortunately, these methods do not lend themselves well to hand calculation.