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ArcSin




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.12.06.0071.01









  


  








Input Form





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





2007-05-02