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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Continued fraction representations





http://functions.wolfram.com/01.30.10.0001.01









  


  










Input Form





ArcSech[z] == (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) (Pi/2 - Sqrt[1 - z^(-2)]/ (z (1 - (1 2)/(z^2 (3 - (1 2)/(z^2 (5 - (3 4)/(z^2 (7 - (3 4)/(z^2 (9 - (5 6)/(z^2 (11 - \[Ellipsis]))))))))))))) /; !IntervalMemberQ[Interval[{-1, 1}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "z"], "-", "1"]]], " "]], SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]]], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["-", "1"]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["-", "2"]]]]]]]], RowBox[List["1", "-", FractionBox[RowBox[List["1", "\[Times]", "2", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["3", "-", FractionBox[RowBox[List["1", "\[Times]", "2", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["5", "-", FractionBox[RowBox[List["3", " ", "\[Times]", "4", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["7", "-", FractionBox[RowBox[List["3", " ", "\[Times]", "4", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["9", "-", FractionBox[RowBox[List["5", " ", "\[Times]", "6", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["11", "-", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]], ")"]]]]]], "/;", "\[InvisibleSpace]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]], "\[InvisibleSpace]"]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "z"], "-", "1"]]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["z", "2"]]]]], RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", FractionBox["2", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["3", "-", FractionBox["2", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["5", "-", FractionBox[RowBox[List["3", " ", "4"]], RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["3", " ", "4"]], RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["9", "-", FractionBox[RowBox[List["5", " ", "6"]], RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["11", "-", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29