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ArcSinh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.27.1222.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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










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





2003-08-21