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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/07.33.03.0795.01









  


  








Input Form





HypergeometricU[11/2, -3, -z] == -((1/(32564156625 Sqrt[Pi])) ((128 z (z (-2835 + z (-6615 + 8 z (-46305 + z (59535 + 2 z (-12315 + z (2121 + 4 (-39 + z) z)))))) BesselK[0, z/2] + (-11340 + z (-26460 + z (-46305 + 8 z (-13230 + z (40395 + 2 z (-10416 + z (1971 + 4 (-38 + z) z))))))) BesselK[1, z/2] - (z (-2835 + z (-6615 + 8 z (-46305 + z (59535 + 2 z (-12315 + z (2121 + 4 (-39 + z) z)))))) BesselI[0, z/2] + (11340 + z (26460 + z (46305 - 8 z (-13230 + z (40395 + 2 z (-10416 + z (1971 + 4 (-38 + z) z))))))) BesselI[1, z/2]) (Log[-z] - Log[z])))/E^(z/2)))








Standard Form





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MathML Form







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<mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 38 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1971 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10416 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40395 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 13230 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 26460 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11340 </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'> -3 </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'> 32564156625 </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'> 128 </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 </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -39 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 2121 </cn> </apply> </apply> <cn type='integer'> -12315 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> -46305 </cn> </apply> </apply> <cn type='integer'> -6615 </cn> </apply> </apply> <cn type='integer'> -2835 </cn> </apply> <apply> <ci> BesselK </ci> 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type='integer'> -11340 </cn> </apply> <apply> <ci> BesselK </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -39 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 2121 </cn> </apply> </apply> <cn type='integer'> -12315 </cn> </apply> </apply> <cn type='integer'> 59535 </cn> </apply> </apply> <cn type='integer'> -46305 </cn> </apply> </apply> 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type='integer'> 40395 </cn> </apply> </apply> <cn type='integer'> -13230 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 26460 </cn> </apply> </apply> <cn type='integer'> 11340 </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 type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02