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 ArcCoth

 http://functions.wolfram.com/01.28.16.0068.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04