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 ArcCoth

 http://functions.wolfram.com/01.28.27.1134.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04