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DifferenceDelta

Compute the forward difference f[x + h] - f[x] of an expression.

$ wo 'DifferenceDelta[x^2, x]'
1 + 2*x

A rational summand is combined over a common denominator.

$ wo 'DifferenceDelta[1/(2 n + 1), n]'
-2/((1 + 2*n)*(3 + 2*n))

With a numeric step the polynomial result is factored.

$ wo 'DifferenceDelta[x^2 + x, x]'
2*(1 + x)