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 Pi

 http://functions.wolfram.com/02.03.06.0007.01

 Input Form

 Pi == -2 Log[1 + Sqrt[2]] + 4 Sqrt[2] Sum[(-1)^k/(4 k + 1), {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["2"]]], " ", "]"]]]], "+", RowBox[List["4", SqrtBox["2"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List[RowBox[List["4", "k"]], "+", "1"]]]]]]]]]]]]]

 MathML Form

 π 4 2 k = 0 ( - 1 ) k 4 k + 1 - 2 log ( 1 + 2 ) 4 2 1 2 k 0 -1 k 4 k 1 -1 -1 2 1 2 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["2"]]], "]"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List[RowBox[List["4", " ", "k"]], "+", "1"]]]]]]]]]]]]]

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

 2001-10-29