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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Complex characteristics > Conjugate value





http://functions.wolfram.com/01.28.19.0007.01









  


  










Input Form





Conjugate[ArcCoth[x + I y]] == (1/4) (2 I ArcTan[1 - x/(x^2 + y^2), y/(x^2 + y^2)] - 2 I ArcTan[1 + x/(x^2 + y^2), -(y/(x^2 + y^2))] - Log[(1 - 2 x + x^2 + y^2)/(x^2 + y^2)] + Log[(1 + 2 x + x^2 + y^2)/(x^2 + y^2)])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Conjugate", "[", RowBox[List["ArcCoth", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox["x", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]], ",", FractionBox["y", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox["x", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]], ",", RowBox[List["-", FractionBox["y", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]]]], "]"]]]], "-", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", RowBox[List["2", " ", "x"]], "+", SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]], RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", RowBox[List["2", " ", "x"]], "+", SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]], RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]], "]"]]]], ")"]]]]]]]]










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





2001-10-29





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