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ArcCoth




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Representations through equivalent functions > With related functions > Involving sec-1 > Involving coth-1(z) > Involving coth-1(z) and sec-1((2(z2-1)1/2/((z2-1)1/2-z))1/2)





http://functions.wolfram.com/01.28.27.1628.01









  


  








Input Form





ArcCoth[z] == 2 Sqrt[z^2] Sqrt[-(1/z^2)] Sqrt[1 - z] Sqrt[1/(1 - z)] ArcSec[Sqrt[(2 Sqrt[z^2 - 1])/(Sqrt[z^2 - 1] - z)]] + (1 + ((I Sqrt[z])/2) Sqrt[-(1/z)] + ((I Sqrt[z^2])/(2 Sqrt[z])) Sqrt[-(1/z)] - Sqrt[1 - z] Sqrt[1/(1 - z)]) Pi I








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]], " ", RowBox[List["ArcSec", "[", SqrtBox[FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "-", "z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox["z"]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], RowBox[List["2", " ", SqrtBox["z"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]]]]]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]]


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





2003-09-04