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 ArcCsch

 http://functions.wolfram.com/01.29.27.0988.01

 Input Form

 ArcCsch[Sqrt[(2 z)/(-z - 1)]] == (-(Sqrt[-z]/2)) Sqrt[1/z] (ArcCsc[z] + Pi/2)

 Standard Form

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

 MathML Form

 csch - 1 ( 2 z - z - 1 ) - 1 2 - z 1 z ( csc - 1 ( z ) + π 2 ) 2 z -1 z -1 -1 1 2 -1 1 2 -1 z 1 2 1 z -1 1 2 z 2 -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[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", SqrtBox[RowBox[List["-", "z"]]]]], ")"]], " ", SqrtBox[FractionBox["1", "z"]], " ", RowBox[List["(", RowBox[List[RowBox[List["ArcCsc", "[", "z", "]"]], "+", FractionBox["\[Pi]", "2"]]], ")"]]]]]]]]

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

 2003-08-21