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http://functions.wolfram.com/03.01.03.0007.01
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BesselJ[1/3, z] == (3 AiryAi[-((3/2)^(2/3) z^(2/3))] -
Sqrt[3] AiryBi[-((3/2)^(2/3) z^(2/3))])/(2^(2/3) 3^(1/3) z^(1/3))
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Cell[BoxData[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "3"], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["3", " ", RowBox[List["AiryAi", "[", RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], ")"]]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["AiryBi", "[", RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], ")"]]]], "]"]]]]]], RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["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> <msub> <mi> J </mi> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mtext> </mtext> </mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mn> 3 </mn> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BesselJ </ci> <cn type='rational'> 1 <sep /> 3 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> AiryAi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselJ", "[", RowBox[List[FractionBox["1", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["3", " ", RowBox[List["AiryAi", "[", RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], ")"]]]], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["AiryBi", "[", RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], ")"]]]], "]"]]]]]], RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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