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http://functions.wolfram.com/03.08.21.0066.01
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Integrate[z^(\[Alpha] - 1) BesselK[\[Nu], (2/3) (a z^r)^(3/2)]
AiryBiPrime[a z^r], z] ==
(-(1/r)) ((2^(-(5/3) - \[Nu]) 3^(-(5/6) - \[Nu]) Sqrt[Pi] z^\[Alpha]
Csc[Pi \[Nu]] (4^\[Nu] ((a z^r)^(3/2))^(2 \[Nu])
MeijerG[{{(1/6) (2 - 3 \[Nu]), (1/6) (5 - 3 \[Nu]),
1 - \[Alpha]/(3 r) - \[Nu]/2}, {1/3}},
{{0, 2/3}, {1/3, 2/3 - \[Nu], -\[Nu], -((2 \[Alpha] + 3 r \[Nu])/
(6 r))}}, (-(2/3)^(2/3)) a z^r, 1/3] -
9^\[Nu] MeijerG[{{1 - \[Alpha]/(3 r) + \[Nu]/2, (1/6) (2 + 3 \[Nu]),
(1/6) (5 + 3 \[Nu])}, {1/3}}, {{0, 2/3},
{1/3, -(\[Alpha]/(3 r)) + \[Nu]/2, \[Nu], 2/3 + \[Nu]}},
(-(2/3)^(2/3)) a z^r, 1/3]))/((a z^r)^(3/2))^\[Nu])
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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> <msup> <mi> z </mi> <mrow> <mi> α </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> K </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <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> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <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> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> r </mi> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( 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3 </mn> <mo> ⁢ </mo> <mi> r </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["2", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", "a", " ", SuperscriptBox["z", "r"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["3", " ", "\[Nu]"]]]], ")"]]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "6"], " ", 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</cn> <cn type='rational'> 5 <sep /> 6 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <ci> α </ci> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <ci> ν </ci> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <plus /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 9 </cn> <ci> ν </ci> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> ν </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> ν </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <plus /> <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> <times /> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> ν </ci> <apply> <plus /> <ci> ν </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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