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 Factorial

 http://functions.wolfram.com/06.01.07.0001.01

 Input Form

 n! == Integrate[t^n/E^t, {t, 0, Infinity}] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", "!"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t", "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", " ", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 n ! 0 t n - t t /; n Condition n t 0 t n -1 t n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["n_", "!"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t", "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29