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 ArcSin

 http://functions.wolfram.com/01.12.27.1395.01

 Input Form

 ArcSin[Sqrt[(z^2 + 1)/z^2]] == Pi/2 - z^2 Sqrt[-z^(-4)] ArcCosh[Sqrt[z^(-2) + 1]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]], SuperscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[SuperscriptBox["z", "2"], SqrtBox[RowBox[List["-", SuperscriptBox["z", RowBox[List["-", "4"]]]]]], RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List[SuperscriptBox["z", RowBox[List["-", "2"]]], "+", "1"]]], "]"]], " "]]]]]]]]

 MathML Form

 sin - 1 ( z 2 + 1 z 2 ) π 2 - z 2 - 1 z 4 cosh - 1 ( 1 + 1 z 2 ) z 2 1 z 2 -1 1 2 2 -1 -1 z 2 -1 1 z 4 -1 1 2 1 1 z 2 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]], SuperscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[SuperscriptBox["z", "2"], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List[FractionBox["1", SuperscriptBox["z", "2"]], "+", "1"]]], "]"]]]]]]]]]]

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

 2003-08-21