AiryAi[z] AiryAiPrime[z] == (-(1/(4 Pi^(3/2)))) MeijerG[{{}, {1/2}}, {{0, 1/3, 2/3}, {}}, (2/3)^(2/3) z, 1/3]

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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> <mrow> <mi> Ai </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Ai </mi> <mo> &#8242; </mo> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;3&quot;]], RowBox[List[&quot;3&quot;, &quot;,&quot;, &quot;0&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;2&quot;, &quot;3&quot;], &quot;)&quot;]], RowBox[List[&quot;2&quot;, &quot;/&quot;, &quot;3&quot;]]], &quot; &quot;, &quot;z&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;3&quot;], MeijerG, Rule[Editable, True]]]], MeijerG], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;3&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;2&quot;, &quot;3&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <times /> <ci> Ai </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <partialdiff /> <ci> Ai </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list /> </list> <apply> <times /> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29