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 Pi

 http://functions.wolfram.com/02.03.06.0043.01

 Input Form

 Pi == 4 Sum[((-1)^k Cos[(2 k + 1) x])/(2 k + 1), {k, 0, Infinity}] /; Element[x, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", "x"]], "]"]]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

 MathML Form

 π 4 k = 0 ( - 1 ) k cos ( ( 2 k + 1 ) x ) 2 k + 1 /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition 4 k 0 -1 k 2 k 1 x 2 k 1 -1 x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", "x"]], "]"]]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

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

 2001-10-29