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SphericalBesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Linear arguments





http://functions.wolfram.com/03.21.21.0016.01









  


  








Input Form





Integrate[(z^(\[Alpha] - 1) SphericalBesselJ[\[Nu], a z])/E^(I a z), z] == ((2^(-1 - \[Nu]) Sqrt[Pi] z^\[Alpha] (a z)^\[Nu])/ ((\[Alpha] + \[Nu]) Gamma[3/2 + \[Nu]])) HypergeometricPFQ[{1 + \[Nu], \[Alpha] + \[Nu]}, {1 + \[Alpha] + \[Nu], 2 + 2 \[Nu]}, -2 I a z]








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[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a_", " ", "z_"]]], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["a_", " ", "z_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "\[Alpha]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], "\[Nu]"]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List["\[Alpha]", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Alpha]", "+", "\[Nu]"]], ",", RowBox[List["2", "+", RowBox[List["2", " ", "\[Nu]"]]]]]], "}"]], ",", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]]]]]]]


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





2007-05-02