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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/03.21.21.0002.01









  


  










Input Form





Integrate[SphericalBesselJ[\[Nu], z], z] == 2^(-2 - \[Nu]) Sqrt[Pi] z^(1 + \[Nu]) Gamma[(1 + \[Nu])/2] HypergeometricPFQRegularized[ {(1 + \[Nu])/2}, {3/2 + \[Nu], (3 + \[Nu])/2}, -(z^2/4)]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "+", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", FractionBox[RowBox[List["3", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]]]]]]










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





2007-05-02