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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=9/2





http://functions.wolfram.com/07.33.03.0698.01









  


  








Input Form





HypergeometricU[9/2, -(11/2), z] == (1/24385536000) (-2 Sqrt[z] (-1091475 + 2 z (628425 + 8 z (-59535 + 2 z (19845 + z (-13965 + 2 z (6615 + 4 z (2805 + z (754 + z (69 + 2 z))))))))) + E^z Sqrt[Pi] (1091475 + 4 z (-496125 + z (496125 + 8 z (-47250 + z (33075 + 4 z (-6615 + z (11025 + 2 z (6300 + z (1575 + 4 z (35 + z)))))))))) Erfc[Sqrt[z]])








Standard Form





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MathML Form







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</mo> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <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> <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 </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> <mn> 4 </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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 69 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 754 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2805 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 6615 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 13965 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 19845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 59535 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 628425 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1091475 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='rational'> 9 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 24385536000 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <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'> 4 </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> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 35 </cn> </apply> </apply> <cn type='integer'> 1575 </cn> </apply> </apply> <cn type='integer'> 6300 </cn> </apply> </apply> <cn type='integer'> 11025 </cn> </apply> </apply> <cn type='integer'> -6615 </cn> </apply> </apply> <cn type='integer'> 33075 </cn> </apply> </apply> <cn type='integer'> -47250 </cn> </apply> </apply> <cn type='integer'> 496125 </cn> </apply> </apply> <cn type='integer'> -496125 </cn> </apply> </apply> <cn type='integer'> 1091475 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <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> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 69 </cn> </apply> </apply> <cn type='integer'> 754 </cn> </apply> </apply> <cn type='integer'> 2805 </cn> </apply> </apply> <cn type='integer'> 6615 </cn> </apply> </apply> <cn type='integer'> -13965 </cn> </apply> </apply> <cn type='integer'> 19845 </cn> </apply> </apply> <cn type='integer'> -59535 </cn> </apply> </apply> <cn type='integer'> 628425 </cn> </apply> </apply> <cn type='integer'> -1091475 </cn> </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