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 ArcCsch

 http://functions.wolfram.com/01.29.27.0159.01

 Input Form

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

 Standard Form

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

 MathML Form

 csch - 1 ( - 2 z z - 1 ) z 2 - z ( π 2 - sin - 1 ( 1 z ) ) -2 z 1 2 z -1 1 2 -1 z 1 2 2 -1 z 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[RowBox[List["-", "2"]], " ", "z_"]]], SqrtBox[RowBox[List["z_", "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcSin", "[", FractionBox["1", "z"], "]"]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "z"]]]]]]]]]]

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

 2003-08-21