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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Specific values > Specialized values > For fixed z > Explicit rational nu





http://functions.wolfram.com/03.21.03.0007.01









  


  










Input Form





SphericalBesselJ[-(25/6), z] == (Sqrt[Pi]/(54 2^(1/6) 3^(5/6) z^(25/6))) (9 Sqrt[3] z^(4/3) (-160 + 9 z^2) AiryAi[(-(3/2)^(2/3)) z^(2/3)] - 60 2^(1/3) 3^(1/6) (-32 + 9 z^2) AiryAiPrime[(-(3/2)^(2/3)) z^(2/3)] + 9 z^(4/3) (160 - 9 z^2) AiryBi[(-(3/2)^(2/3)) z^(2/3)] + 20 2^(1/3) 3^(2/3) (-32 + 9 z^2) AiryBiPrime[(-(3/2)^(2/3)) z^(2/3)])










Standard Form





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MathML Form







<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> <mrow> <mo> - </mo> <mfrac> <mn> 25 </mn> <mn> 6 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <mroot> <mn> 2 </mn> <mn> 6 </mn> </mroot> <mo> &#8290; </mo> <msup> <mn> 3 </mn> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 160 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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</mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mroot> <mn> 3 </mn> <mn> 6 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 32 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Ai </mi> <mo> &#8242; </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> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <msup> <mn> 3 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 32 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </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> &#8290; </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> SphericalBesselJ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 25 <sep /> 6 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 54 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 6 </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'> 25 <sep /> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </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'> -160 </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'> 9 </cn> <apply> <plus /> <cn type='integer'> 160 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </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'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </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'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -32 </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> <apply> <times /> <cn type='integer'> 20 </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'> 2 <sep /> 3 </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'> -32 </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>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalBesselJ", "[", RowBox[List[RowBox[List["-", FractionBox["25", "6"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["9", " ", SqrtBox["3"], " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "160"]], "+", 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["60", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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["9", " ", SuperscriptBox["z", RowBox[List["4", "/", "3"]]], " ", RowBox[List["(", RowBox[List["160", "-", 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["20", " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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["54", " ", SuperscriptBox["2", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["z", RowBox[List["25", "/", "6"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





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