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 ArcCoth

 http://functions.wolfram.com/01.28.27.2742.01

 Input Form

 ArcCoth[(1 + z)/(2 Sqrt[z])] == 2 ArcTanh[1/Sqrt[z]] + Pi Sqrt[z] Sqrt[-(1/z)] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["2", SqrtBox["z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "+", RowBox[List["\[Pi]", " ", SqrtBox["z"], SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

 coth - 1 ( 1 + z 2 z ) 2 tanh - 1 ( 1 z ) + π - 1 z z /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition 1 z 2 z 1 2 -1 2 1 z 1 2 -1 -1 1 z -1 1 2 z 1 2 z 1 [/itex]

 Rule Form

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

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

 2003-09-04