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ArcCosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.27.1406.01









  


  










Input Form





ArcCosh[Sqrt[z - Sqrt[z^2 - 1]]/Sqrt[2 z]] == ((-Sqrt[z]) Sqrt[-(1/z)] + I Sqrt[(-I) z] Sqrt[I/z] - I Sqrt[-z^2 + 1] Sqrt[1/(-z^2 + 1)]) ((-(1/2)) Sqrt[I/z] Sqrt[1/z] Sqrt[(-I) z] Sqrt[z] Sqrt[1/(1 + z)] Sqrt[1 + z] (Pi/2 - ArcSec[z]) + (Pi/4) (2 + ((-z + Sqrt[z^2])/Sqrt[z/(1 + z)]) Sqrt[1/z] Sqrt[1/(1 + z)]))










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_", "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]]], SqrtBox[RowBox[List["2", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["z"]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SqrtBox[FractionBox["\[ImaginaryI]", "z"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", "1"]]], " ", SqrtBox[FractionBox["1", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", "1"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SqrtBox[FractionBox["\[ImaginaryI]", "z"]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcSec", "[", "z", "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "z"]], "+", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]]]], SqrtBox[FractionBox["z", RowBox[List["1", "+", "z"]]]]]]], ")"]]]]]], ")"]]]]]]]]










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





2003-08-21