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 ArcCsch

 http://functions.wolfram.com/01.29.27.1338.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21