Factorial: Representations through equivalent functions (formula 06.01.27.0004)

Factorial

$Mathematica Notation$

Gamma, Beta, Erf

Factorial[n]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/06.01.27.0004.01

Input Form

n! == (n - 1)!! n!!

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["n", "!"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!!"]], " ", RowBox[List["n", "!!"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> !! </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> n </mi> <mo> !! </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <times /> <apply> <ci> Factorial2 </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Factorial2 </ci> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["n_", "!"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!!"]], " ", RowBox[List["n", "!!"]]]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29

Factorial2[n]