HypergeometricU[4, -4, z] == (1/241920) (144 + z (-144 + z (120 + z (-120 + z (210 + z (146 + z (23 + z)))))) + E^z z^5 (336 + z (168 + z (24 + z))) (CoshIntegral[z] - SinhIntegral[z]))

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<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> 4 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 241920 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <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> 24 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 168 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 336 </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> 5 </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> <mi> z </mi> <mo> + </mo> <mn> 23 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 146 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 210 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 144 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 144 </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'> -4 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 241920 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 24 </cn> </apply> </apply> <cn type='integer'> 168 </cn> </apply> </apply> <cn type='integer'> 336 </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'> 5 </cn> </apply> </apply> <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 /> <ci> z </ci> <cn type='integer'> 23 </cn> </apply> </apply> <cn type='integer'> 146 </cn> </apply> </apply> <cn type='integer'> 210 </cn> </apply> </apply> <cn type='integer'> -120 </cn> </apply> </apply> <cn type='integer'> 120 </cn> </apply> </apply> <cn type='integer'> -144 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 144 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02