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 Sin

 http://functions.wolfram.com/01.06.23.0010.01

 Input Form

 Sum[((-1)^(k - 1) Sin[k x])/k, {k, 1, Infinity}] == x/2 /; Abs[Re[x]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["k", " ", "x"]], "]"]]]], "k"]]], "\[Equal]", FractionBox["x", "2"]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "x", "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 k = 1 ( - 1 ) k - 1 sin ( k x ) k x 2 /; "\[LeftBracketingBar]" Re ( x ) "\[RightBracketingBar]" < π Condition k 1 -1 k -1 k x k -1 x 2 -1 x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k_", "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["k_", " ", "x_"]], "]"]]]], "k_"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["x", "2"], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "x", "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2001-10-29