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 ArcCoth

 http://functions.wolfram.com/01.28.16.0056.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04