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 ArcSin

 http://functions.wolfram.com/01.12.27.1726.01

 Input Form

 ArcSin[z] == Sqrt[z^(-2)] ((Pi z)/2) - (Sqrt[-z]/Sqrt[z]) ArcCoth[Sqrt[z^2/(z^2 - 1)]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SqrtBox[SuperscriptBox["z", RowBox[List["-", "2"]]]], FractionBox[RowBox[List["\[Pi]", " ", "z"]], "2"]]], "-", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox["z"]], RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]]]]]]]]

 MathML Form

 sin - 1 ( z ) π z 2 1 z 2 - - z z coth - 1 ( z 2 z 2 - 1 ) z z 2 -1 1 z 2 -1 1 2 -1 -1 z 1 2 z 1 2 -1 z 2 z 2 -1 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "z"]], ")"]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", "z"]]], " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]], SqrtBox["z"]]]]]]]]

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

 2003-08-21