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 | | http://functions.wolfram.com/03.07.26.0023.01 | 
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 | | AiryAiPrime[3^(2/3) z^(1/3)] Hypergeometric0F1[b, z] == 
 (-(1/Pi^(3/2))) 2^(-(8/3) + b) 3^(1/6) Gamma[b] 
  MeijerG[{{(1/6) (5 - 3 b), (1/6) (8 - 3 b)}, {}}, 
   {{0, 2/3}, {1 - b, 5/3 - b}}, 4 z] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAiPrime", "[", RowBox[List[SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["b", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["8", "3"]]], "+", "b"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["3", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["3", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["5", "3"], "-", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]]]]]] | 
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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>  <msup>  <mi> Ai </mi>  <mo> ′ </mo>  </msup>  <mo> ( </mo>  <mrow>  <msup>  <mn> 3 </mn>  <mrow>  <mn> 2 </mn>  <mo> / </mo>  <mn> 3 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 3 </mn>  </mroot>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 0 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mo>   </mo>  <mo> ; </mo>  <mi> b </mi>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["0", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["b", Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric0F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] </annotation>  </semantics>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mrow>  <msup>  <mn> 2 </mn>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mfrac>  <mn> 8 </mn>  <mn> 3 </mn>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mroot>  <mn> 3 </mn>  <mn> 6 </mn>  </mroot>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> b </mi>  <mo> ) </mo>  </mrow>  </mrow>  <msup>  <mi> π </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mfrac>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mn> 4 </mn>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 6 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 5 </mn>  <mo> - </mo>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> , </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 6 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 8 </mn>  <mo> - </mo>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mfrac>  <mn> 2 </mn>  <mn> 3 </mn>  </mfrac>  <mo> , </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> b </mi>  </mrow>  <mo> , </mo>  <mrow>  <mfrac>  <mn> 5 </mn>  <mn> 3 </mn>  </mfrac>  <mo> - </mo>  <mi> b </mi>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["4", " ", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["3", " ", "b"]]]], ")"]]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["3", " ", "b"]]]], ")"]]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "b"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["5", "3"], "-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <times />  <apply>  <ci> AiryAiPrime </ci>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 3 </cn>  <cn type='rational'> 2 <sep /> 3 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Hypergeometric0F1 </ci>  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 8 <sep /> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 3 </cn>  <cn type='rational'> 1 <sep /> 6 </cn>  </apply>  <apply>  <ci> Gamma </ci>  <ci> b </ci>  </apply>  <apply>  <power />  <apply>  <power />  <pi />  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <apply>  <times />  <cn type='rational'> 1 <sep /> 6 </cn>  <apply>  <plus />  <cn type='integer'> 5 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> b </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 6 </cn>  <apply>  <plus />  <cn type='integer'> 8 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> b </ci>  </apply>  </apply>  </apply>  </apply>  </list>  <list />  </list>  <list>  <list>  <cn type='integer'> 0 </cn>  <cn type='rational'> 2 <sep /> 3 </cn>  </list>  <list>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  <apply>  <plus />  <cn type='rational'> 5 <sep /> 3 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  </list>  </list>  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["AiryAiPrime", "[", RowBox[List[SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z_", RowBox[List["1", "/", "3"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["b_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["8", "3"]]], "+", "b"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["3", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["3", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["5", "3"], "-", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]], SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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