A relation between consecutive elements of a sequence. The first difference is D u(n) = u(n+1) - u(n) where u(n) is the nth element of sequence u. The second difference is D2 u(n) = D (D u(n)) = (u(n+2) - u(n+1)) - (u(n+1) - u(n)) = u(n+2) - 2u(n+1) + u(n) And so on. A recurrence relation such as u(n+2) + a u(n+1) + b u(n) = 0 can be converted to a difference equation (in this case, a second order linear difference equation): D2 u(n) + p D u(n) + q u(n) = 0 and vice versa. a, b, p, q are constants. (1995-02-10)
