FactorialPower[x, n]
gives the factorial power .

FactorialPower[x, n, h]
gives the step-h factorial power .


  • Mathematical function, suitable for both symbolic and numeric manipulation.
  • For integer n, is given by , and is given by .
  • is given for any n by .
  • TemplateBox[{TemplateBox[{x, k}, FactorialPower], x}, DifferenceDelta2] is given by k TemplateBox[{x, {k, -, 1}}, FactorialPower] and sum_xTemplateBox[{x, k}, FactorialPower] is given by TemplateBox[{x, {k, +, 1}}, FactorialPower]/(k+1).
  • FactorialPower[x, n] evaluates automatically only when x and n are numbers.
  • FunctionExpand always converts FactorialPower to a polynomial or combination of gamma functions.
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