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 ArcCoth

 http://functions.wolfram.com/01.28.27.2113.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04