html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Factorial

 http://functions.wolfram.com/06.01.17.0004.01

 Input Form

 n! == (-1)^m Pochhammer[-n, m] (n - m)! /; Element[m, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", "!"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "n"]], ",", "m"]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]], "!"]]]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]

 MathML Form

 n ! ( - 1 ) m ( - n ) m TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "n"]], ")"]], "m"], Pochhammer] ( n - m ) ! /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition n -1 m Pochhammer -1 n m n -1 m m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["n_", "!"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "n"]], ",", "m"]], "]"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]], "!"]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29