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 ArcCoth

 http://functions.wolfram.com/01.28.27.2117.01

 Input Form

 ArcCoth[1/Sqrt[z]] == ArcSinh[Sqrt[-z]/Sqrt[z - 1]] /; Element[z, Reals] && 0 < z < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", "z", "<", "1"]]]], ")"]]]]]]

 MathML Form

 coth - 1 ( 1 z ) sinh - 1 ( - z z - 1 ) /; ( z 0 < z < 1 ) Condition 1 z 1 2 -1 -1 z 1 2 z -1 1 2 -1 z 0 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[RowBox[List["-", "z"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", "z", "<", "1"]]]]]]]]]]

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

 2003-09-04