Difference Equations and Other Functional Equations

Let yn = y(n) be a function of integer argument n = 0, 1, 2, . . . A first-order homogeneous linear difference equation has the form

yn+1 + anyn = 0. (17.1.1.1) Its general solution can be written in the form

yn = Cun, un = (–1)na0a1 . . . an-1, n = 1, 2, . . . , (17.1.1.2) where C = y0 is an arbitrary constant and un is a particular solution.