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http://functions.wolfram.com/03.07.07.0005.01
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AiryAiPrime[z] == (Pi/9) (((3^(1/3) z^2)/(2 Pi I))
ContourIntegral[Gamma[s]/(Gamma[1/2 + s] Gamma[5/3 - s] Gamma[1/2 - s])/
(z^3/9)^s, \[ScriptCapitalL]["s"]] - ((3 3^(2/3))/(2 Pi I))
ContourIntegral[Gamma[s]/(Gamma[1/2 + s] Gamma[1/3 - s] Gamma[1/2 - s])/
(z^3/9)^s, \[ScriptCapitalL]["s"]])
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Cell[BoxData[RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "9"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "3"]]], SuperscriptBox["z", "2"]]], RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " "]], RowBox[List[" ", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["5", "3"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]]]], SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]], "-", RowBox[List[FractionBox[RowBox[List["3", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]], RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " "]], RowBox[List[" ", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "3"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]]]], SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "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> <mfrac> <mi> π </mi> <mn> 9 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <msup> <mn> 3 </mn> <mrow> <mn> 1 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <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> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 5 </mn> <mn> 3 </mn> </mfrac> <mo> - 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</ms> <ms> s </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 2 </ms> </apply> <ms> - </ms> <ms> s </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> 3 </ms> </apply> <ms> 9 </ms> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <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> <ms> ) </ms> </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["1", "9"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["5", "3"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]], ")"]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "3"], "9"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "3"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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