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 ArcCsch

 http://functions.wolfram.com/01.29.27.0344.01

 Input Form

 ArcCsch[Sqrt[-2 z]/Sqrt[z - 1]] == (-(I/2)) ArcCos[1/z] /; Inequality[-Pi, Less, Arg[z], LessEqual, 0]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsch", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "2"]], "z"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["\[ImaginaryI]", "2"]]], RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]

 MathML Form

 csch - 1 ( - 2 z z - 1 ) - 1 2 cos - 1 ( 1 z ) /; - π < arg ( z ) 0 Condition -2 z 1 2 z -1 1 2 -1 -1 1 2 1 z -1 Inequality -1 z 0 [/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]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21