Provide FactorialPower as a Basis for Discrete Calculus
FactorialPower plays the same role in discrete calculus that Power does in continuous calculus, including simple derivatives and intetegrals and the basis for a standard series representation.
 In[1]:= ```{D[Power[x, n], x], DifferenceDelta[FactorialPower[x, n], x]} // TraditionalForm```

 In[2]:= ```{Integrate[Power[x, n], x], Sum[FactorialPower[x, n], x]} // TraditionalForm```

 In[3]:= ```{Sum[(D[1 + 2 x + 3 x^2, {x, k}] /. x -> x0) Power[x - x0, k]/k!, {k, 0, 2}], Sum[(DifferenceDelta[1 + 2 x + 3 x^2, {x, k}] /. x -> x0) FactorialPower[x - x0, k]/k!, {k, 0, 2}]}```
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 In[4]:= ```{Sum[(D[1 + 2 x + 3 x^2, {x, k}] /. x -> x0) Power[x - x0, k]/k!, {k, 0, 2}], Sum[(DifferenceDelta[1 + 2 x + 3 x^2, {x, k}] /. x -> x0) FactorialPower[x - x0, k]/k!, {k, 0, 2}]}; First[%] - Last[%] // FunctionExpand // Expand```
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 In[5]:= ```Plot[Evaluate@Table[FactorialPower[x, k], {k, 1, 4}], {x, 0, 5}, PlotRange -> {-1.1, 2}]```
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