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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.17.03.0008.01









  


  










Input Form





KelvinBei[-(11/3), z] == (-(1/(27 3^(5/6) z^(11/3)))) (20 (-1)^(1/4) 2^(2/3) ((9/160) Sqrt[3] ((1 + I) z)^(4/3) (-160 + 9 I z^2) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (9/160) Sqrt[3] ((1 + I) z)^(4/3) (160 I - 9 z^2) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (3/4) 3^(1/6) (32 - 9 I z^2) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (3/4) 3^(1/6) (-32 I + 9 z^2) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (9 ((1 + I) z)^(4/3) - (81/160) I z^2 ((1 + I) z)^(4/3)) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (-9 I ((1 + I) z)^(4/3) + (81/160) z^2 ((1 + I) z)^(4/3)) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + (1/4) 3^(2/3) (-32 + 9 I z^2) AiryBiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + (1/4) 3^(2/3) (32 I - 9 z^2) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]))










Standard Form





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MathML Form







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<mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <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> 32 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mo> - </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mn> 3 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> 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encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinBei </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 3 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 5 <sep /> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 160 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 160 </cn> <imaginaryi /> </apply> <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> AiryAi </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 160 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <imaginaryi /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <cn type='integer'> 3 </cn> <apply> 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<times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> </apply> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 81 <sep /> 160 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> 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Rule Form





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





2007-05-02





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