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ArcSin




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/01.12.26.0004.01









  


  








Input Form





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