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Sign






Mathematica Notation

Traditional Notation









Complex Components > Sign[z] > Limit representations





http://functions.wolfram.com/12.06.09.0002.01









  


  










Input Form





Sign[x] == Limit[((4 (m + 1) (2 n + 1))/Pi) x (HypergeometricPFQ[{-m, m + 2, -n + 1/2, n + 3/2}, {3/2, 3/2, 3/2}, x^2]/ HypergeometricPFQ[{-n, n + 1, -m - 1/2, m + 3/2}, {1/2, 1, 1}, x^2]), n + m -> Infinity] /; -1 < x < 1 && Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]], ")"]]]], ")"]], " ", "x", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "m"]], ",", RowBox[List["m", "+", "2"]], ",", RowBox[List[RowBox[List["-", "n"]], "+", FractionBox["1", "2"]]], ",", RowBox[List["n", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", SuperscriptBox["x", "2"]]], "]"]]]], RowBox[List["\[Pi]", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List["n", "+", "1"]], ",", RowBox[List[RowBox[List["-", "m"]], "-", FractionBox["1", "2"]]], ",", RowBox[List["m", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "1"]], "}"]], ",", SuperscriptBox["x", "2"]]], "]"]]]]], ",", RowBox[List[RowBox[List["n", "+", "m"]], "\[Rule]", "\[Infinity]"]]]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "x", "<", "1"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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