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 ArcCsch

 http://functions.wolfram.com/01.29.27.1379.01

 Input Form

 ArcCsch[Sqrt[-((2 z)/(I + z))]] == (Pi I)/4 - (1/2) ArcSinh[1/z] /; Re[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsch", "[", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["2", "z"]], RowBox[List["\[ImaginaryI]", "+", "z"]]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSinh", "[", FractionBox["1", "z"], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 csch - 1 ( - 2 z + z ) π 4 - 1 2 sinh - 1 ( 1 z ) /; Re ( z ) < 0 Condition -1 2 z z -1 1 2 4 -1 -1 1 2 1 z -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["2", " ", "z_"]], RowBox[List["\[ImaginaryI]", "+", "z_"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSinh", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21