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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Representations through equivalent functions > With related functions > Involving tan-1 > Involving csch-1(21/2 (1+z2)1/4/(z-(1+z2)1/2)1/2) > Involving csch-1(21/2 (1+z2)1/4/(z-(1+z2)1/2)1/2) and tan-1(1/z)





http://functions.wolfram.com/01.29.27.0620.01









  


  










Input Form





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










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





2003-08-21