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ArcCsc




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.17.27.0807.01









  


  








Input Form





ArcCsc[(Sqrt[2] (1 + z^2)^(1/4))/Sqrt[Sqrt[1 + z^2] - z]] == ArcCot[z]/2 - (Pi/4) (Sqrt[z^2]/z - 1) /; !IntervalMemberQ[Interval[{-1, Infinity}], I z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsc", "[", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["1", "/", "4"]]]]], SqrtBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["ArcCot", "[", "z", "]"]], "2"], "-", RowBox[List[FractionBox["\[Pi]", "4"], RowBox[List["(", RowBox[List[FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"], "-", "1"]], ")"]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "\[Infinity]"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "]"]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z_", "2"]]], ")"]], RowBox[List["1", "/", "4"]]]]], SqrtBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]], "-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["ArcCot", "[", "z", "]"]], "2"], "-", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"], "-", "1"]], ")"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "\[Infinity]"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]


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





2003-08-21