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 ArcCsch

 http://functions.wolfram.com/01.29.27.0153.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21