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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=4





http://functions.wolfram.com/07.33.03.0650.01









  


  








Input Form





HypergeometricU[4, -5, z] == (1/2177280) (720 - z (576 + z (-360 + z (240 + z (30 + z (12 + z)) (-7 + z (14 + z))))) - E^z z^6 (504 + z (216 + z (27 + 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> 4 </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> 2177280 </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> <mi> z </mi> <mo> + </mo> <mn> 27 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 216 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 504 </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> <mi> z </mi> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 14 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 360 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 576 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 720 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 4 </cn> <cn type='integer'> -5 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2177280 </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 /> <ci> z </ci> <cn type='integer'> 27 </cn> </apply> </apply> <cn type='integer'> 216 </cn> </apply> </apply> <cn type='integer'> 504 </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 /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <cn type='integer'> 30 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 14 </cn> </apply> </apply> <cn type='integer'> -7 </cn> </apply> </apply> <cn type='integer'> 240 </cn> </apply> </apply> <cn type='integer'> -360 </cn> </apply> </apply> <cn type='integer'> 576 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 720 </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