Using Generating Functions to Solve Linear Inhomogeneous Recurrence Equations

Abstract: This paper looks at the approach of using generating functions to solve linear inhomogeneous recurrence equations with constant coefficients. It will be shown that the generating functions for these recurrence equations are rational functions. By decomposing a generating function into partial fractions, one can derive explicit formula as well as asymptotic estimates for its coefficients. Key–Words: Linear recurrence equations, generating functions, partial fractions decomposition.