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ArcSec




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.18.27.0487.01









  


  








Input Form





ArcSec[(z^2 + 1)/(z^2 - 1)] == Pi - ((2 Sqrt[z^2])/z) ArcTan[z] /; !IntervalMemberQ[Interval[{-Infinity, -1}], I z] && !IntervalMemberQ[Interval[{1, Infinity}], I z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSec", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "]"]], "\[Equal]", RowBox[List["\[Pi]", "-", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]]]], "z"], RowBox[List["ArcTan", "[", "z", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", " ", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", 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["ArcSec", "[", FractionBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]], RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["ArcTan", "[", "z", "]"]]]], "z"]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]]]


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





2003-08-21