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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=5





http://functions.wolfram.com/07.33.03.0748.01









  


  








Input Form





HypergeometricU[5, -5, z] == (1/87091200) (2880 - z (2880 + z (-2160 + z (1680 + z (-1680 + z (3024 + z (2414 + z (502 + z (39 + z)))))))) - E^z z^6 (5040 + z (2880 + z (540 + z (40 + z)))) (CoshIntegral[z] - SinhIntegral[z]))








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 87091200 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> </mrow> <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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 40 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 540 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2880 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5040 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </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> <mrow> <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> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 39 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 502 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2414 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3024 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2160 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2880 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2880 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 5 </cn> <cn type='integer'> -5 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 87091200 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 40 </cn> </apply> </apply> <cn type='integer'> 540 </cn> </apply> </apply> <cn type='integer'> 2880 </cn> </apply> </apply> <cn type='integer'> 5040 </cn> </apply> <apply> <plus /> <apply> <ci> CoshIntegral </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> SinhIntegral </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 39 </cn> </apply> </apply> <cn type='integer'> 502 </cn> </apply> </apply> <cn type='integer'> 2414 </cn> </apply> </apply> <cn type='integer'> 3024 </cn> </apply> </apply> <cn type='integer'> -1680 </cn> </apply> </apply> <cn type='integer'> 1680 </cn> </apply> </apply> <cn type='integer'> -2160 </cn> </apply> </apply> <cn type='integer'> 2880 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2880 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02