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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 trigonometric functions and a power function > Involving sin and power > Power arguments





http://functions.wolfram.com/03.21.21.0032.01









  


  










Input Form





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










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"]]], " ", RowBox[List["Sin", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]]]], "]"]]]], 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", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["1", "+", "\[Nu]"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", RowBox[List["2", " ", "r"]]], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox["\[Alpha]", RowBox[List["2", " ", "r"]]], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["r", "+", "\[Alpha]", "+", RowBox[List["r", " ", "\[Nu]"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], "]"]]]]]]]]]










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





2007-05-02