Linear difference equation

Summary

A linear difference equation is a recurrence in which the unknown sequence appears only linearly: $a_k(n) u_{n+k} + \dots + a_0(n) u_n = b(n)$. The coefficients may depend on $n$; when they are constant one gets a linear recurrence with constant coefficients. Its solutions have the same structure as those of a linear differential equation. The solutions of the homogeneous equation form a vector space, and the general solution is one particular solution plus a homogeneous solution.