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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/07.33.03.0787.01









  


  








Input Form





HypergeometricU[11/2, -5, -z] == -( (256 z (8 z (-14175 + z (-22680 + z (-22680 + z (-19845 + 2 z (-158760 + z (155925 + 4 z (-12264 + z (1641 + 2 (-48 + z) z)))))))) BesselK[0, z/2] + (-453600 + z (-725760 + z (-739935 + 8 z (-82215 + 2 z (-39690 + z (-59535 + 2 z (57813 + 2 z (-10761 + 2 z (774 + (-47 + z) z))))))))) BesselK[1, z/2] - (8 z (-14175 + z (-22680 + z (-22680 + z (-19845 + 2 z (-158760 + z (155925 + 4 z (-12264 + z (1641 + 2 (-48 + z) z)))))))) BesselI[0, z/2] + (453600 + z (725760 + z (739935 - 8 z (-82215 + 2 z (-39690 + z (-59535 + 2 z (57813 + 2 z (-10761 + 2 z (774 + (-47 + z) z))))))))) BesselI[1, z/2]) (Log[-z] - Log[z])))/ E^(z/2)/(12993098493375 Sqrt[Pi]))








Standard Form





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MathML Form







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<mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 155925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 158760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 19845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 22680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 22680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 14175 </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 739935 </mn> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z 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<plus /> <ci> z </ci> <cn type='integer'> -48 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 1641 </cn> </apply> </apply> <cn type='integer'> -12264 </cn> </apply> </apply> <cn type='integer'> 155925 </cn> </apply> </apply> <cn type='integer'> -158760 </cn> </apply> </apply> <cn type='integer'> -19845 </cn> </apply> </apply> <cn type='integer'> -22680 </cn> </apply> </apply> <cn type='integer'> -22680 </cn> </apply> </apply> <cn type='integer'> -14175 </cn> </apply> <apply> <ci> BesselK </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <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 /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> 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type='integer'> -22680 </cn> </apply> </apply> <cn type='integer'> -14175 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <cn type='integer'> 739935 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <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'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -47 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 774 </cn> </apply> </apply> <cn type='integer'> -10761 </cn> </apply> </apply> <cn type='integer'> 57813 </cn> </apply> </apply> <cn type='integer'> -59535 </cn> </apply> </apply> <cn type='integer'> -39690 </cn> </apply> </apply> <cn type='integer'> -82215 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 725760 </cn> </apply> </apply> <cn type='integer'> 453600 </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