The backward difference is a finite difference defined by del _p congruent del f_p congruent f_p - f_(p - 1). Higher order differences are obtained by repeated operations of the backward difference operator, so del _p^2 | = | del ( del p) = del (f_p - f_(p - 1)) = del f_p - del f_(p - 1) | = | (f_p - f_(p - 1)) - (f_(p - 1) - f_(p - 2)) | = | f_p - 2f_(p - 1) + f_(p - 2). In general, del _p^k congruent del ^k f_p congruent sum_(m = 0)^k (-1)^m(k m) f_(p - m), where (k m) is a binomial coefficient.
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