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ArcCosh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Representations through equivalent functions > With related functions > Involving cos-1 > Involving cosh-1((z+a)1/2/(2 z)1/2) > Involving cosh-1((z+1)1/2/(2 z)1/2) and cos-1(1/z)





http://functions.wolfram.com/01.26.27.0324.01









  


  








Input Form





ArcCosh[Sqrt[z + 1]/Sqrt[2 z]] == ((z Sqrt[1 - z])/2) Sqrt[1/(1 - z)] Sqrt[-(1/z^2)] (Pi/2 - ArcCos[1/z]) + (Pi/4) ((-z) Sqrt[-z^(-2)] - I Sqrt[1 - z] Sqrt[1/(1 - z)] - I + 2 I Sqrt[(z + 1)/z] Sqrt[z/(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["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List["z_", "+", "1"]]], SqrtBox[RowBox[List["2", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["z", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]]]], "-", "\[ImaginaryI]", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]], " ", SqrtBox[FractionBox["z", RowBox[List["z", "+", "1"]]]]]]]], ")"]]]]]]]]]]


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





2003-08-21