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 Sin

 http://functions.wolfram.com/01.06.23.0020.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02