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 ArcCoth

 http://functions.wolfram.com/01.28.27.3490.01

 Input Form

 ArcCoth[Sqrt[z^2 - 1]/Sqrt[z^2]] == ArcSech[1/z] - (Pi I)/2 /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], SqrtBox[SuperscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 coth - 1 ( z 2 - 1 z 2 ) sech - 1 ( 1 z ) - π 2 /; 0 arg ( z ) < π Condition z 2 -1 1 2 z 2 1 2 -1 1 z -1 -1 2 -1 Inequality 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], SqrtBox[SuperscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-09-04