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difference equation

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)