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 ArcCsch

 http://functions.wolfram.com/01.29.16.0011.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21