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variants of this functions
KelvinBer




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.18.03.0036.01









  


  








Input Form





KelvinBer[13/3, z] == (z^(4/3) (Sqrt[6] ((1 + I) z)^(1/3) (4480 - 3024 I z^2 - 81 z^4) AiryAi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + Sqrt[6] ((1 + I) z)^(1/3) (-4480 I + 3024 z^2 + 81 I z^4) AiryAi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 168 (-1)^(1/4) 3^(1/6) z (80 - 9 I z^2) AiryAiPrime[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] - 168 (-1)^(1/4) 3^(1/6) z (-80 I + 9 z^2) AiryAiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + Sqrt[2] ((1 + I) z)^(1/3) (-4480 + 3024 I z^2 + 81 z^4) AiryBi[(-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + Sqrt[2] ((1 + I) z)^(1/3) (4480 I - 3024 z^2 - 81 I z^4) AiryBi[(1/2) 3^(2/3) ((1 + I) z)^(2/3)] + 56 (-1)^(3/4) 3^(2/3) z (80 I + 9 z^2) AiryBiPrime[ (-(1/2)) 3^(2/3) ((1 + I) z)^(2/3)] + 56 (-1)^(1/4) 3^(2/3) z (-80 I + 9 z^2) AiryBiPrime[(1/2) 3^(2/3) ((1 + I) z)^(2/3)]))/ (108 3^(5/6) ((1 + I) z)^(2/3) ((-1)^(1/4) z)^(16/3))








Standard Form





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MathML Form







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</mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> <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> <mrow> <mn> 80 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Ai </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> <mn> 168 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mroot> <mn> 3 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Rule Form





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





2007-05-02