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http://functions.wolfram.com/03.01.03.0037.01
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BesselJ[14/3, z] == (288 Sqrt[3] z^(4/3) (-110 + 9 z^2)
AiryAi[(-(3/2)^(2/3)) z^(2/3)] + 3 2^(1/3) 3^(1/6)
(14080 - 4320 z^2 + 81 z^4) AiryAiPrime[(-(3/2)^(2/3)) z^(2/3)] +
288 z^(4/3) (-110 + 9 z^2) AiryBi[(-(3/2)^(2/3)) z^(2/3)] +
2^(1/3) 3^(2/3) (14080 - 4320 z^2 + 81 z^4)
AiryBiPrime[(-(3/2)^(2/3)) z^(2/3)])/(81 2^(2/3) 3^(5/6) z^(14/3))
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Cell[BoxData[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[FractionBox["14", "3"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["288", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "110"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["3", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List["14080", "-", RowBox[List["4320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["81", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "110"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["AiryBi", "[", 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["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["14080", "-", RowBox[List["4320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["81", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["81", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["14", "/", "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> 14 </mn> <mn> 3 </mn> </mfrac> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 81 </mn> <mo> ⁢ </mo> <msup> <mn> 2 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 3 </mn> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 14 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 288 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 110 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <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> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 288 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 110 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <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> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mn> 3 </mn> <mn> 6 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 81 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 14080 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Ai </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <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> </mrow> <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> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> ⁢ </mo> <msup> <mn> 3 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 81 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 14080 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <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> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </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'> 14 <sep /> 3 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 81 </cn> <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'> 5 <sep /> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 14 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 288 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -110 </cn> </apply> <apply> <ci> AiryAi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 288 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -110 </cn> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 14080 </cn> </apply> <apply> <ci> AiryAiPrime </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 14080 </cn> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 3 </cn> </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["14", "3"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["288", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "110"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["AiryAi", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["3", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List["14080", "-", RowBox[List["4320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["81", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]], "+", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "110"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["AiryBi", "[", 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["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List["14080", "-", RowBox[List["4320", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["81", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]], "]"]]]]]], RowBox[List["81", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["14", "/", "3"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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