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 Pi

 http://functions.wolfram.com/02.03.09.0007.01

 Input Form

 Pi == 16 Limit[(n + 1) Product[k^2/(2 k + 1)^2, {k, 1, n}], n -> Infinity]

 Standard Form

 Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["16", " ", RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], FractionBox[SuperscriptBox["k", "2"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]]]

 MathML Form

 π 16 lim n "\[Rule]" ( n + 1 ) k = 1 n k 2 ( 2 k + 1 ) 2 16 n n n 1 k 1 n k 2 2 k 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List["16", " ", RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], FractionBox[SuperscriptBox["k", "2"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]]]

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

 2001-10-29