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 ArcCsch

 http://functions.wolfram.com/01.29.27.0084.01

 Input Form

 ArcCsch[z] == z Sqrt[-z^(-2)] (-(Pi/2) + ArcSin[Sqrt[(z^2 + 1)/z^2]])

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21