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ArcCosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.27.0026.02









  


  








Input Form





ArcCosh[(2 z)/(z^2 + 1)] == (Sqrt[-(1 - z)^2]/(1 - z)) (2 ArcCot[z] - Pi/2) /; (Abs[z] <= 1 && Inequality[-(Pi/2), LessEqual, Arg[z], Less, Pi/2]) || (Abs[z] > 1 && !IntervalMemberQ[Interval[{-Infinity, -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["ArcCosh", "[", FractionBox[RowBox[List["2", " ", "z_"]], RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcCot", "[", "z", "]"]]]], "-", FractionBox["\[Pi]", "2"]]], ")"]]]], RowBox[List["1", "-", "z"]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[LessEqual]", "1"]], "&&", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]]]


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





2001-10-29