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ArcCot






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.16.27.1373.01









  


  










Input Form





ArcCot[(2 Sqrt[z^2 - 1])/(z^2 - 2)] == (Pi/2) (z/Sqrt[-1 + z^2]) Sqrt[1 - 1/z^2] (-2 + Sqrt[I/z] Sqrt[(-I) z] - Sqrt[-(I/z)] Sqrt[I z] + Sqrt[1/z^2] z - Sqrt[(-1 + z)/z] Sqrt[z/(-1 + z)] + Sqrt[1 + 1/z] Sqrt[z/(1 + z)]) + 2 (z/Sqrt[-1 + z^2]) Sqrt[1 - 1/z^2] ArcSec[z]










Standard Form





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MathML Form







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Rule Form





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










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





2003-08-21