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 Pi

 http://functions.wolfram.com/02.03.09.0004.01

 Input Form

 Pi == Limit[(2^(4 n + 1) n!^4)/((2 n + 1) (2 n)!^2), n -> Infinity]

 Standard Form

 Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["4", " ", "n"]], "+", "1"]]], " ", SuperscriptBox[RowBox[List["n", "!"]], "4"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]], "!"]], "2"]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

 MathML Form

 π lim n "\[Rule]" 2 4 n + 1 n ! 4 ( 2 n + 1 ) ( 2 n ) ! 2 n n 2 4 n 1 n 4 2 n 1 2 n 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["4", " ", "n"]], "+", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["n", "!"]], ")"]], "4"]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["2", " ", "n"]], ")"]], "!"]], ")"]], "2"]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

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

 2001-10-29