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 ArcSech

 http://functions.wolfram.com/01.30.27.1670.01

 Input Form

 ArcSech[Sqrt[z/(z + 1)]] == -ArcSinh[1/Sqrt[z]] /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", SqrtBox[FractionBox["z", RowBox[List["z", "+", "1"]]]], "]"]], "\[Equal]", " ", RowBox[List["-", RowBox[List["ArcSinh", "[", FractionBox["1", SqrtBox["z"]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 sech - 1 ( z z + 1 ) - sinh - 1 ( 1 z ) /; ( z z < - 1 ) Condition z z 1 -1 1 2 -1 1 z 1 2 -1 z z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", SqrtBox[FractionBox["z_", RowBox[List["z_", "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["ArcSinh", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-08-21