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ArcCsch






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.29.27.1880.01









  


  










Input Form





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










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





2003-08-21