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http://functions.wolfram.com/03.21.21.0045.01
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Integrate[SphericalBesselJ[\[Mu], a z^r] SphericalBesselJ[\[Nu], a z^r],
z] == ((2^(-2 - \[Mu] - \[Nu]) Pi z (a z^r)^(\[Mu] + \[Nu]))/
((1 + r (\[Mu] + \[Nu])) Gamma[3/2 + \[Mu]] Gamma[3/2 + \[Nu]]))
HypergeometricPFQ[{1 + \[Mu]/2 + \[Nu]/2, 3/2 + \[Mu]/2 + \[Nu]/2,
1/(2 r) + \[Mu]/2 + \[Nu]/2}, {3/2 + \[Mu], 1 + 1/(2 r) + \[Mu]/2 +
\[Nu]/2, 3/2 + \[Nu], 2 + \[Mu] + \[Nu]}, (-a^2) z^(2 r)]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <mrow> <msub> <mi> j </mi> <mi> μ </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> j </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo>  </mo> <mrow> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> <mo> - </mo> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> μ </mi> <mo> + 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<msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "4"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Mu]", "2"], "+", FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Mu]", "2"], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Mu]", "2"], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["1", RowBox[List["2", " ", "r"]]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], 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type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <ci> μ </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 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Date Added to functions.wolfram.com (modification date)
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