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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(z1/2) > Involving coth-1(z1/2) and sin-1(2 (-z)1/2/1-z)





http://functions.wolfram.com/01.28.27.0131.01









  


  








Input Form





ArcCoth[Sqrt[z]] == (-((Sqrt[-z^2] (1 + z))/(2 (z (1 - z))))) Sqrt[((1 - z)/(1 + z))^2] ArcSin[(2 Sqrt[-z])/(1 - z)] - ((Pi Sqrt[z])/4) Sqrt[-(1/z)] (1 + ((1 + z)/(1 - z)) Sqrt[((1 - z)/(1 + z))^2]) /; 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", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[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["1", "-", "z"]]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]], ")"]]]]]]], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", SqrtBox["z"]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", 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["Abs", "[", "z", "]"]], "\[NotEqual]", "1"]]]]]]]]


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





2003-09-04