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 ArcSin

 http://functions.wolfram.com/01.12.27.0488.01

 Input Form

 ArcSin[(2 z)/(z^2 + 1)] == Pi z Sqrt[z^(-2)] - 2 ArcTan[1/z] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", " ", "z", SqrtBox[SuperscriptBox["z", RowBox[List["-", "2"]]]]]], "-", RowBox[List["2", " ", RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

 sin - 1 ( 2 z z 2 + 1 ) π z 1 z 2 - 2 tan - 1 ( 1 z ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition 2 z z 2 1 -1 z 1 z 2 -1 1 2 -1 2 1 z -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["2", " ", "z_"]], RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[Pi]", " ", "z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]]]], "-", RowBox[List["2", " ", RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2003-08-21