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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/01.30.06.0062.01









  


  








Input Form





ArcSech[z]^2 \[Proportional] Log[2/z]^2 - ((Log[2/z] z^2)/2) (1 + (3 z^2)/8 + (5 z^4)/24 + O[z^6]) + (z^4/16) (1 + (3 z^2)/4 + (107 z^4)/192 + O[z^6]) /; (z -> 0)








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"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", FractionBox["2", "z"], "]"]], " ", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["3", " ", SuperscriptBox["z", "2"]]], "8"], "+", FractionBox[RowBox[List["5", " ", SuperscriptBox["z", "4"]]], "24"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "6"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["3", " ", SuperscriptBox["z", "2"]]], "4"], "+", FractionBox[RowBox[List["107", " ", SuperscriptBox["z", "4"]]], "192"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "6"]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]


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





2007-05-02