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ArcSinh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.27.0818.01









  


  








Input Form





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


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





2003-08-21