Cosh[(2 z^(3/2))/3] AiryAi[z] == (2/3)^(1/6) Pi MeijerG[{{}, {5/12, 11/12}}, {{0, 1/3}, {1/2, 5/6}}, (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> cosh </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mi> Ai </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mtext> </mtext> <mo> &#10869; </mo> <mrow> <mroot> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mn> 6 </mn> </mroot> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </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> <mrow> <mfrac> <mn> 5 </mn> <mn> 12 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 12 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 6 </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;2&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;2&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[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;12&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;11&quot;, &quot;12&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;1&quot;, &quot;2&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;6&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> cosh </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <ci> Ai </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <pi /> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='rational'> 5 <sep /> 12 </cn> <cn type='rational'> 11 <sep /> 12 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 5 <sep /> 6 </cn> </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