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 ArcCsch

 http://functions.wolfram.com/01.29.27.1426.01

 Input Form

 ArcCsch[Sqrt[2]/Sqrt[Sqrt[1 + z^2] - 1]] == ArcSinh[z]/2 /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsch", "[", FractionBox[SqrtBox["2"], SqrtBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "-", "1"]]]], " ", "]"]], "\[Equal]", FractionBox[RowBox[List["ArcSinh", "[", "z", "]"]], "2"]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", FractionBox[SqrtBox["2"], SqrtBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]], "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["ArcSinh", "[", "z", "]"]], "2"], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21