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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > For fixed z > For fixed z and a=11/2





http://functions.wolfram.com/07.33.03.0783.01









  


  








Input Form





HypergeometricU[11/2, -6, -z] == -( (256 z (z (-1360800 + z (-1927800 + z (-1647135 + 8 z (-144585 + z (-99225 + 2 z (-530145 + z (467775 + 4 z (-32871 + z (3957 - 210 z + 4 z^2))))))))) BesselK[0, z/2] + (-5443200 + z (-7711200 + z (-6758640 + z (-4867695 + 8 z (-422415 + z (-337365 + 2 z (-218295 + z (357639 + 4 z (-29217 + z (3753 - 206 z + 4 z^2)))))))))) BesselK[1, z/2] - (z (-1360800 + z (-1927800 + z (-1647135 + 8 z (-144585 + z (-99225 + 2 z (-530145 + z (467775 + 4 z (-32871 + z (3957 - 210 z + 4 z^2))))))))) BesselI[0, z/2] + (5443200 + z (7711200 + z (6758640 + z (4867695 - 8 z (-422415 + z (-337365 + 2 z (-218295 + z (357639 + 4 z (-29217 + z (3753 - 206 z + 4 z^2)))))))))) BesselI[1, z/2]) (Log[-z] - Log[z])))/E^(z/2)/(298841265347625 Sqrt[Pi]))








Standard Form





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MathML Form







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<mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 210 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 3957 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 32871 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 467775 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 530145 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 99225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 144585 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1647135 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1927800 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1360800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> 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</mo> <mn> 357639 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 218295 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 337365 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 422415 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6758640 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 7711200 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5443200 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> -6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 298841265347625 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z 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<apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 206 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3753 </cn> </apply> </apply> <cn type='integer'> -29217 </cn> </apply> </apply> <cn type='integer'> 357639 </cn> </apply> </apply> <cn type='integer'> -218295 </cn> </apply> </apply> <cn type='integer'> -337365 </cn> </apply> </apply> <cn type='integer'> -422415 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 6758640 </cn> </apply> </apply> <cn type='integer'> 7711200 </cn> </apply> </apply> <cn type='integer'> 5443200 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn 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Rule Form





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





2007-05-02