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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.30.06.0067.01









  


  










Input Form





ArcSech[z]^2 == Log[2/z]^2 - (z^2/2) Log[2/z] HypergeometricPFQ[{3/2, 1, 1}, {2, 2}, z^2] + (z^4/16) HypergeometricPFQ[{3/2, 1, 1}, {2, 2}, z^2]^2 /; !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", "[", SuperscriptBox[RowBox[List["ArcSech", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Log", "[", FractionBox["2", "z"], "]"]], "2"], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Log", "[", FractionBox["2", "z"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2"]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["z", "4"], " ", SuperscriptBox[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2"]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]], "2"]]]]], "/;", 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)





2007-05-02





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