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ArcCsc






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.17.27.1457.01









  


  










Input Form





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










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





2003-08-21