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 ArcCsch

 http://functions.wolfram.com/01.29.16.0106.01

 Input Form

 ArcCsch[Sqrt[1/(-1 - z^2)]] == (Pi I)/2 - ArcCsch[1/z] /; Pi/2 < Arg[z] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsch", "[", SqrtBox[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "-", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcCsch", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 csch - 1 ( 1 - 1 - z 2 ) π 2 - csch - 1 ( 1 z ) /; π 2 < arg ( z ) < π Condition 1 -1 -1 z 2 -1 1 2 2 -1 -1 1 z -1 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", SqrtBox[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "-", SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcCsch", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21