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 ArcCsch

 http://functions.wolfram.com/01.29.27.0518.01

 Input Form

 ArcCsch[Sqrt[1 + z]/Sqrt[-z]] == I ArcTan[Sqrt[z]] /; Inequality[-Pi, Less, Arg[z], LessEqual, 0]

 Standard Form

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

 MathML Form

 csch - 1 ( 1 + z - z ) tan - 1 ( z ) /; - π < arg ( z ) 0 Condition 1 z 1 2 -1 z 1 2 -1 z 1 2 Inequality -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", FractionBox[SqrtBox[RowBox[List["1", "+", "z_"]]], SqrtBox[RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21