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 Cos

 http://functions.wolfram.com/01.07.23.0023.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["Cos", "[", RowBox[List["k", " ", "x"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["DiracComb", "[", FractionBox["x", RowBox[List["2", "\[Pi]"]]], "]"]]]], "-", FractionBox["1", "2"]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], RowBox[List["Cos", "[", RowBox[List["k_", " ", "x_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["DiracComb", "[", FractionBox["x", RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "-", FractionBox["1", "2"]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

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

 2007-05-02