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ArcCoth




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Representations through equivalent functions > With related functions > Involving sin-1 > Involving coth-1(1/z1/2) > Involving coth-1(1/z1/2) and sin-1(2 (-z)1/2/z-1)





http://functions.wolfram.com/01.28.27.0212.01









  


  








Input Form





ArcCoth[1/Sqrt[z]] == ((Sqrt[-z^2] (1 + z))/(2 z (1 - z))) Sqrt[((1 - z)/(1 + z))^2] ArcSin[(2 Sqrt[-z])/(z - 1)] - (1 - ((1 + z)/(1 - z)) Sqrt[((1 - z)/(1 + z))^2]) ((Pi Sqrt[-z^2])/(4 z)) /; Abs[z] != 1








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], ")"]], "2"]], " ", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List["-", "z"]]]]], RowBox[List["z", "-", "1"]]], "]"]]]], RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], ")"]], "2"]]]], RowBox[List["1", "-", "z"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], ")"]]]], RowBox[List["4", " ", "z"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[NotEqual]", "1"]]]]]]]]


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





2003-09-04