FactorialPower

FactorialPower[x,n]
gives the factorial power .

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

DetailsDetails

  • 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.
Introduced in 2008
(7.0)