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ArcSinh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Representations through equivalent functions > With related functions > Involving tanh-1 > Involving sinh-1(((z-(z2-1)1/2)/(2(z2-1)1/2))1/2) > Involving sinh-1(((z-(z2-1)1/2)/(2(z2-1)1/2))1/2) and tanh-1(1/z)





http://functions.wolfram.com/01.25.27.1481.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", RowBox[List["ArcTanh", "[", FractionBox["1", "z"], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["z"]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]"]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", SqrtBox[SuperscriptBox["z", "2"]]]], SqrtBox["z"]]]], ")"]]]]]]]]]]


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





2003-08-21