Solutions of linear recurrence equations

摘要

Solutions are given to general homogeneous and non-homogeneous recurrence equations defined on the set of integers. Solutions to homogeneous recurrence equations are given as: (i) an infinite series of terms involving the partial ordinary Bell polynomial; (ii) an infinite series of terms involving the complete ordinary Bell polynomial; (iii) a weighted finite sum of terms involving powers. Solutions to non-homogeneous recurrence equations are given as: (i) a finite series of terms involving the complete ordinary Bell polynomial; (ii) a weighted infinite sum of terms involving powers. Computational issues of these solutions are also discussed.