A GENERALIZED SOLUTION EXPRESSION FOR LINEAR HOMOGENEOUS CONSTANT-COEFFICIENT DIFFERENCE-EQUATIONS

We present here what is, to our knowledge, a completely new and genera l solution expression for the complementary solution of an arbitary Nt h order linear homogeneous constant-coefficient difference equation wh ich, unlike the solution expressions usually presented in textbooks, d oes not a priori assert the specific structural form of the solution. This method easily handles the case of repeated zero roots, a case of practical importance for which the classical solution expression fails , as recently shown by Johnson. Furthermore, we show that both the cla ssical solution expression, and Johnson's ''singular solution'' expres sion for the present an example illustrating the interrelationships am ongst the different solution expressions as well as the solution obtai ned via the generating-function method.