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 ArcSinh

 http://functions.wolfram.com/01.25.27.1724.01

 Input Form

 ArcSinh[Sqrt[(z - Sqrt[z^2 - 1])/(2 Sqrt[z^2 - 1])]] == (1/2) ArcCoth[z] /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List["z", "-", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], RowBox[List["2", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCoth", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 sinh - 1 ( z - z 2 - 1 2 z 2 - 1 ) 1 2 coth - 1 ( z ) /; Re ( z ) > 0 Condition z -1 z 2 -1 1 2 2 z 2 -1 1 2 -1 1 2 1 2 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["ArcCoth", "[", "z", "]"]], "2"], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2003-08-21