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http://functions.wolfram.com/03.07.07.0004.01
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AiryAiPrime[z] == (-(3^(1/6)/(2 Pi))) (1/(2 Pi I))
ContourIntegral[(Gamma[s] Gamma[s + 2/3])/(z/3^(2/3))^(3 s),
\[ScriptCapitalL]["s"]]
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Cell[BoxData[RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["3", RowBox[List["1", "/", "6"]]], RowBox[List["2", " ", "\[Pi]"]]]]], FractionBox["1", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["2", "3"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["3", RowBox[List[RowBox[List["-", "2"]], "/", "3"]]], " ", "z"]], ")"]], RowBox[List[RowBox[List["-", "3"]], "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]
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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> <msup> <mi> Ai </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mroot> <mn> 3 </mn> <mn> 6 </mn> </mroot> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mo> ∫ </mo> <mi> ℒ </mi> </msub> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mn> 3 </mn> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> s </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> Ai </ms> <ms> ′ </ms> </apply> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RadicalBox </ci> <ms> 3 </ms> <ms> 6 </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> π </ms> </list> </apply> </apply> </list> </apply> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> π </ms> <ms> ⅈ </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> ∫ </ms> </apply> <ms> ℒ </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <ms> s </ms> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> s </ms> <ms> + </ms> <apply> <ci> FractionBox </ci> <ms> 2 </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> 3 </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> 2 </ms> </list> </apply> <ms> / </ms> <ms> 3 </ms> </list> </apply> </apply> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> 3 </ms> </list> </apply> <ms> s </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ⅆ </ms> <ms> s </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["2", "3"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["3", RowBox[List[RowBox[List["-", "2"]], "/", "3"]]], " ", "z"]], ")"]], RowBox[List[RowBox[List["-", "3"]], " ", "s"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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