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 ArcCoth

 http://functions.wolfram.com/01.28.27.2040.01

 Input Form

 ArcCoth[Sqrt[z]] == ArcSinh[Sqrt[1/(z - 1)]] /; !IntervalMemberQ[Interval[{-Infinity, 1}], z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List["ArcSinh", "[", SqrtBox[FractionBox["1", RowBox[List["z", "-", "1"]]]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "1"]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]]]]

 MathML Form

 coth - 1 ( z ) sinh - 1 ( 1 z - 1 ) /; z ( - , 1 ) coth - 1 ( z ) sinh - 1 ( 1 z - 1 ) /; z ( - , 1 ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox[FractionBox["1", RowBox[List["z", "-", "1"]]]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]

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

 2003-09-04