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 ArcSinh

 http://functions.wolfram.com/01.25.27.1723.01

 Input Form

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

 Standard Form

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

 MathML Form

 sinh - 1 ( 1 - 1 - z 2 2 1 - z 2 ) z 2 2 z coth - 1 ( 1 z ) 1 -1 1 -1 z 2 1 2 2 1 -1 z 2 1 2 -1 1 2 z 2 1 2 2 z -1 1 z -1 [/itex]

 Rule Form

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

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

 2003-08-21