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 ArcCsch

 http://functions.wolfram.com/01.29.27.1386.01

 Input Form

 ArcCsch[Sqrt[(2 z)/(-z - 1)]] == Sqrt[-z] Sqrt[1/z] ((I/2) ArcSinh[I/z] - Pi/4)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCsch", "[", SqrtBox[FractionBox[RowBox[List["2", "z"]], RowBox[List[RowBox[List["-", "z"]], "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[FractionBox["1", "z"]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["ArcSinh", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]], "-", FractionBox["\[Pi]", "4"]]], ")"]]]]]]]]

 MathML Form

 csch - 1 ( 2 z - z - 1 ) - z 1 z ( 1 2 sinh - 1 ( z ) - π 4 ) 2 z -1 z -1 -1 1 2 -1 z 1 2 1 z -1 1 2 1 2 z -1 -1 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", SqrtBox[FractionBox[RowBox[List["2", " ", "z_"]], RowBox[List[RowBox[List["-", "z_"]], "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List["-", "z"]]], " ", SqrtBox[FractionBox["1", "z"]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]], "-", FractionBox["\[Pi]", "4"]]], ")"]]]]]]]]

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

 2003-08-21