|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/03.07.21.0017.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[(z^(\[Alpha] - 1) AiryAiPrime[a z^r])/E^((2/3) (a z^r)^(3/2)),
z] == (z^\[Alpha] (-3 3^(1/3) (2 r + \[Alpha]) Gamma[5/3]
HypergeometricPFQ[{-(1/6), (2 \[Alpha])/(3 r)},
{-(1/3), 1 + (2 \[Alpha])/(3 r)}, (-(4/3)) (a z^r)^(3/2)] +
a^2 z^(2 r) \[Alpha] Gamma[1/3] HypergeometricPFQ[
{7/6, 4/3 + (2 \[Alpha])/(3 r)}, {7/3, 7/3 + (2 \[Alpha])/(3 r)},
(-(4/3)) (a z^r)^(3/2)]))/(3 3^(2/3) \[Alpha] (2 r + \[Alpha])
Gamma[1/3] Gamma[5/3])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "r"]], "+", "\[Alpha]"]], ")"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "6"]]], ",", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]], " ", "\[Alpha]", " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "6"], ",", RowBox[List[FractionBox["4", "3"], "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "3"], ",", RowBox[List[FractionBox["7", "3"], "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["3", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "r"]], "+", "\[Alpha]"]], ")"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> <msup> <mi> ⅇ </mi> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <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> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> Ai </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> <mfrac> <mn> 1 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mn> 3 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> + </mo> <mi> α </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mi> α </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 7 </mn> <mn> 3 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <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> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]], "+", FractionBox["4", "3"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]], "+", FractionBox["7", "3"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mroot> <mn> 3 </mn> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mo> + </mo> <mi> α </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <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> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "6"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "3"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> α </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='integer'> -2 </cn> <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> </apply> <apply> <ci> AiryAiPrime </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <ci> α </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <ci> α </ci> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> α </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> <ci> α </ci> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 7 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </list> <list> <cn type='rational'> 7 <sep /> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 7 <sep /> 3 </cn> </apply> </list> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='integer'> -4 </cn> <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> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <ci> α </ci> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='integer'> -4 </cn> <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> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "r"]], "+", "\[Alpha]"]], ")"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "6"]]], ",", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]], " ", "\[Alpha]", " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "6"], ",", RowBox[List[FractionBox["4", "3"], "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "3"], ",", RowBox[List[FractionBox["7", "3"], "+", FractionBox[RowBox[List["2", " ", "\[Alpha]"]], RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["3", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "r"]], "+", "\[Alpha]"]], ")"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|