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BUILT-IN MATHEMATICA SYMBOL
FactorialPower
FactorialPower[x, n]
gives the factorial power 
.
FactorialPower[x, n, h]
gives the step-h factorial power 
.
Details
- 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]](Files/FactorialPower.en/10.png "TemplateBox[{TemplateBox[{x, k}, FactorialPower], x}, DifferenceDelta2]")
is given by ![k TemplateBox[{x, {k, -, 1}}, FactorialPower]](Files/FactorialPower.en/11.png "k TemplateBox[{x, {k, -, 1}}, FactorialPower]")
and ![sum_xTemplateBox[{x, k}, FactorialPower]](Files/FactorialPower.en/12.png "sum_xTemplateBox[{x, k}, FactorialPower]")
is given by ![TemplateBox[{x, {k, +, 1}}, FactorialPower]/(k+1)](Files/FactorialPower.en/13.png "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.
Examplesopen all
Basic Examples (2)
Find the "factorial square" of 10:
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FactorialPower does not automatically expand out:
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Use FunctionExpand to do the expansion:
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New in 7
