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 ArcCoth

 http://functions.wolfram.com/01.28.27.3428.01

 Input Form

 ArcCoth[Sqrt[z - 1]/Sqrt[z + 1]] == (1/2) ArcSech[1/z] - Sqrt[z] Sqrt[-(1/z)] (Pi/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List["z", "-", "1"]]], SqrtBox[RowBox[List["z", "+", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]]]], "-", RowBox[List[SqrtBox["z"], SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 coth - 1 ( z - 1 z + 1 ) 1 2 sech - 1 ( 1 z ) - 1 2 z - 1 z π z -1 1 2 z 1 1 2 -1 1 2 1 z -1 -1 1 2 z 1 2 -1 1 z -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List["z_", "-", "1"]]], SqrtBox[RowBox[List["z_", "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["z"], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", "\[Pi]"]]]]]]]]

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

 2003-09-04